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So I never found the clue to the second puzzle, rather I tried inputting all the numbers in order, one of which starts with "04378". When I typed that in I thought it somehow solved the puzzle, but when I read your hints here, I found out that it wasn't even the solution and I never even saw puzzle 3.
What happened is "4378" happens to be the solution to the third puzzle, meaning I simply skipped the solution and puzzle 3 by typing the number on a screen in puzzle 2.
All of the numbers match pretty closely, but they aren't identical. There is one "odd number out" in each sequence. ex: the one facing "front" when looking at the keypad reads 73099245. The odd number out is "3", since the number in the second position differs from all the other sequences. The one across from it, with your back to the keypad, reads 78059245. The odd one out here is "5", since all the other sequences have a "9" in that position. By looking at the sequences on our left and right, we can determine which numbers are "supposed to be" in which position, giving us the odd ones out. From the keypad clockwise you should get 3,1,5 ,and 9. Our note from earlier tells us to input in the code from largest number to smallest, so we get 9531.