The kind of puzzle I'd like if where you have 5 switches, and each time you toggle a switch, it will also toggle 1 or 2 other switches. The goal being ofcourse to get all 5 switches on at the same time.
One game I know that has exactly this sort of puzzle is Zork Grand Inquisitor (the Dam puzzle... and even the ultimate solution is theoretically possible in the Oblivion universe). Another that has a similar sort of puzzle is Myst 4: Revelation (I'm thinking of the fireplace puzzle, but the 'reroute-the-power-switches' puzzle might well also apply), but you could probably grab any of the Myst series and find a puzzle of that type somewhere, tbh.
Now, in neither of these games is the toggle 'random' in the sense that you won't know which of the other additional 1 or 2 switches will be toggled when you choose any one of them, but that's not strictly speaking necessary (and would make the puzzle impossible to solve except for luck anyway). My impression, as a person trying to solve such puzzles, is that they're a sort of maze, and solving them requires a sort of mapping skill (which you of course as the author can essentially work backwards to create).
The main thing I would say (for what it's worth), is don't be afraid to be a bit non-linear; the way to make these puzzles difficult relies on a sort of "one step forward, two steps back, then a step to the left, then three steps forward, one step back" kind of maneuver (for example, in the Zork Dam puzzle, one switch opens let's say sluice 4 and 5, another opens sluice 3, but closes sluice 5). Make the user double back and go around to solve the puzzle (but not too much; this is after all an 'action-RPG', not so much a puzzle game
).