Hey everyone. I commented on the map I mentioned above and got a clue from the author. Watahaya couldn't remember fully how it was done, but directed me to Two Tribe's website. After looking at some of the older blog posts from when the game was in beta, I found a comment with the solution.

If you copy an entity in the Toki Tori 2+ level editor, then go into Notepad and choose Edit->Paste, you will see a line like this pasted into your notepad.

"***ENTITIES***: [{"id":147,"props":{},"type":"TokiTori","x":0.0,"y":0.0}]"

Change "TokiTori" to "TokiToriNPC". Then select the whole line and choose Edit->Copy. Now return to the Toki Tori 2+ level editor. Choose Edit->Paste. A TokiToriNPC entity is pasted somewhere. You'll have to find it and drag it into your level where you want to put it. It looks just like a TokiTori entity, except that it has a silly mustache on it.

This trick can presumably be used to get some other entities that aren't normally available in the editor as well. I just wanted to post this to share this info with the Toki Tori 2+ community for everyone else who doesn't know this. And just to be complete, here's a link to the page where I found the comment revealing this information. There are a few other tips in the comments on this page too:

http://twotribes.com/message/toki-tori-2-user-levels/

Thanks for keep this in a thread to remind me :)

You're welcome! :) I wanted it to be easily available for the community.

Tip: If you click "Edit" > "Paste", the new, copied (can be changed too) entity (the Toki Tori NPC) is where you clicked the "Paste" button.

I found a way how to pick another special entities. They aren't from the editor's entity pallette.
Firstly, I pressed the right mouse button on the Toki Tori 2+ (in the Steam games' library). Then I clicked: "Properties" > "Games' local files" > "Browse local files" > "script" folder > "entities" folder. I discovered that most of the names of .bnut files in this folder are also names of the game's entities.
Here's the list of the entities' codes:

***ENTITIES***: [{"id":147,"props":{},"type":"TokiToriNPC","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"LandingStone","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"CollectibleDeposit","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"CollectibleDoor","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"MoleTunnel","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"Mole","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"VisionTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ElevatorDoor","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"FrogApparatus","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ElectricConductor","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"BlurTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"BPMTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"BubbleShip","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"BubbleShipWing","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"CameraShakeTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"Carrot","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"Chestnut","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ColorGradingTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"CycleTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"DebugDoor","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"EnableTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"FireflyNest","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"IntervalTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"LevelBorderBird","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"LevelBorderBirdTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"LevelExit","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"MelodyTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"MusicSource","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ParticlePlayer","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"RaceFinish","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"RaceStart","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"RaceGate","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"RaceOpponent","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"PresentationPlayer","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ReverbTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"SceneCollision","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"SceneCompletedTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"SceneProgressTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ShoeboxIncluder","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ShoeboxTagTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"SoundLayerAreaTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"SoundLayerSettings","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"SoundTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ToasterTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"VibrationTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"AncientFrog_Pipe_Entrance","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"AncientFrogCountTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"AncientFrogCurrentTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"CrystalDestroyer","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"CinematicTokiTori","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ForceAnimationTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ForceMovementTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"BaseEffect","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"ColorGradingEffect","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"MapBirdTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"TokiUnconscious","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"TokiDexCompletionTrigger","x":0.0,"y":0.0}]
***ENTITIES***: [{"id":147,"props":{},"type":"TokiDexPhotoPoint","x":0.0,"y":0.0}]

Some information abot these entities (post #5):
1. If you enter an area of one of the entities with the "level" prop, you'll be directed to the official version of the game. However, if you choose "template_userlevel" in the "level" prop, you will be directed into the example level in the level editor. You can complete that. There will be two levels in one TTLVL file.
2. If you activate an unactivated landing stone or a vision trigger, the same will happen.
3. The race gate changes the shoebox zero. There is a strange background.
4. The Debug Door and the Elevator Door aren't from the official version of the game. They are from the Demo Mode.
5. All Collectible Deposits don't work in the user levels.
6. Crystal Destroyer is the scene characteristic entity so it doesn't work in a user level.

Characteristics of some entities which aren't in the level editor's pallette.

1. Collectible Door - in the official version of the game, it directs you to the wings' room (engineer's house). It opens when all collectibles are in four collectible deposits and you come in front of it.
2. Mole tunnel - it is a passage between two points in the level. Unlike teleporters, you need to press up or down arrow. It activates when you come into one of the entrances (you can choose by using two options: mole dependency and first time opening in Mole entity). It can also be open all the time.
3. Mole - a character which activates a mole tunnel.
4. Vision trigger - in the official version of the game, it displays one of five ancient frog places.
In the level editor, it can be an obstacle.
5. Elevator door - a kind of impractical door. It differs from the TokiDoor (basic door) because the middle part of the door is only 1 square wide.
6. Frog apparatus - a device where one type of an ancient frog permanently attaches to (you can choose).
7. Electric conductor: a slug-like non-moveable beam.
8. Blur trigger: changes the visibility of the foreground and the background in an area.
9. Carrot - a decoration. Reacts with nearby creatures.
10. Chestnut - a decoration and an obstacle. Reacts with nearby creatures.
11. Cycle trigger - cycles activation of other triggers (eg. Enable Trigger).
12. Debug door - instantly teleports you to the matched gate.
13. Enable trigger - enables many effects (effect and triggers entities, music and sounds, fireflies, nests and black geyser). Ideal for cycle triggers, 2 enable triggers (activating and disactivating) and 2 cycle triggers can create a chain.
14. Firefly nest - spawns a new firefly when the one bound to the nest dies.
15. Interval trigger - controls the actions in a cycle, chain or the interactions.
16. Level border bird - is capable of carrying you. When it goes back, it disappears in the place of the first catch. Before disappearing, it can carry other creatures. If it has disappeared, it can't appear again.
17. Level border bird trigger - places the Y level where a level border bird disappears.
18. Level exit - a level exit in the official version of the game.
19. Melody trigger - triggers only when a melody is sung by Toki Tori.
20. Music Source - a music source entity in the official version in the game. Offers more music tracks.
21. Presentation Player - an entity which displays a decoration graphic.
22. Shoebox includer - includes extra objects in the shoebox, for example a mole hill.
23. Sound Layer Area Trigger - enables or disables a sound/music layer.
24. Sound Layer settings - set which layers are active when the level begins.
25. Sound trigger - triggers only when a particular kind of sound is enabled.
26. Cinematic Toki Tori - used as a Toki Tori when the player does not control him in specific scenes (like during destruction of the crystal). Requires Force Movement trigger and/or Force Animation trigger. When there are none of them, it is a Toki Tori controlled by a player.
27. Base effect - changes the intensity of all effects or one effect in an area.
28. Map bird trigger - Allows Toki Tori to be taken by the mapbird when active. In the official version of the game, it is used in crystal destruction scene.
29. Toki Unconscious - an unconscious Toki Tori. Reacts with river currents and Map bird trigger.
30. TokiDex Completion Trigger - in the official version of the game, it triggers when all photos in TokiDex are taken (unlocks the ghost room).
31. TokiDex photo point - a photo entity in TokiDex in the water mountain. It can display a photo taken during the game (in the level editor it doesn't display a taken photo).