OK - I took apart my HP printer I mentioned in my last post and took a peek at the inner workings. Tough one to get the cover off that device... only two easily accessible screws, but four very hard to see plastic snap-thingies. Once discovered, it opens up like a charm though: screw, screw, snap, snap, open.
Even though the gears are plastic ones, I couldn't see any wear or tear (or missing teeth) on any of them. Upon further inspection of the mechanism it turns out that it will turn back and forth the same way when operating. So it should either fail every time or at least hardly ever. Not - like it did - about 50% of the times. I figured it might be some of the sensors telling the electronics where the mechanical parts actually are. Cleaned every one of those, "dusted" off some that I couldn't reach. Also I cleaned out the "ink pit" - you wouldn't believe the amount of dried up ink residue that collects in there after about 14 years of use. Talking about stalactites... or stalagmites... whichever grows ground-up ;P
I'm dirty and got a paper cut while testing it.
Bottom line: it works for now. Will keep on the lookout for a new one though.