After opening it up a little further, this thing is weirder than I thought. It uses some metal wires (not electric), with endstops. Basically pulling on the wire moves it to one direction, and letting it go to its contracted state (presumably by use of some springs) moves it it the opposite direction (with a neutral state somewhere in the middle).
Fortunate thing is that I did manage to find the proper 'neutral' state for left/right, unfortunate thing is that someone else had opened it up before me and didn't close it up properly. Long story short, the up/down array wasn't held together properly so when I opened it up to take a look the parts went everywhere. Took me an hour and a half to figure out which screw and spring went were, and now the up/down isn't quite right.
Still, at least I know what the issue is, so it's just a matter of tweaking it until it works properly.