I've been thinking about it a lot and I kind of imagine that the secret is a bit too obtuse for what it actually pays off with. On that note, it's important to note that you also can just straight up noclip through / remove the locked door if it's too frustrating, the secret will still work in full.

If you're really trying to find the buttons out of some sense of sentimentality, the best way to do that without installing some hacker/entity display mods (which can be found with an easy workshop search) is to enable ent_messages_draw in console, and spam "Clean Up All - Admin". The buttons have a logic entity that runs "Kill" on them at the start of the map, and you can use that to pinpoint all 11 (yeah, it's a lot) possible spawn locations for the buttons. A bit tedious but anyone can do it with some elbow grease.