Okay, so far, no luck.
I have measured the tip and the sleeve of the jack and got a reading in all 3 positions.
I measured the pots itself and I get 12k ohm on both pots. I measured the tone pots and they also seem to work fine, the values increase and decrease with rolling the pots. They both are around the same ballpark, so no big difference between them. As the values can be altered, I think the capacitors are also good?
Then, I found another switch (I think it's even a more expensive Allparts switch) in my parts bin, soldered it in, and exactly the same result. The neck pickup works in the left position, but not in the middle. The bridge doesn't work at all.
So I either have two new switches with the exact same error, or it's not that.
I also recut all the switch and pickup cables to make sure they are not feathered or touching. Also, the switch works fine in a mechanical view, it opens and closes in the right spot and there are no solder bridges.
I should also mention that I have a stereo jack and a killswitch in here. But from a logical point of view, they can't be the problem, because if the killswitch was wired wrong, I wouldn't get anything at all, it's independent from a single pickup. I wired the killswitch so that it grounds the signal when the switch is pressed. This works well.
Oh, I also bridged the skillswitch and soldered in a standard mono jack to the switch earlier. No joy.
Everything else is pretty standard.
I think I'll have a coffee break now =)