Im trying to build up a trek 1100 frame for my brother. Not looking to be period correct or matching or stuff like that. I just want a bike that works. Anyway, will modern 8,9,10 speed derailleurs work with the 7-speed 105 shifters? I imagine the front will work ok but im not sure about the rear because the bike uses a 126mm freewheel hub.
Thanks Guy

most modern 8/9 speed rear derailleurs will work with the 7-speed 105 shifters in combination with a 7 speed shimano/sram/sunrace freewheel. Not all 10 speed rear derailleurs will.

basically just stay away from Shimano Dura-Ace and you should be fine.

OK cool.
Thank You.

+1 Yes. The "brains" are in the indexing lever, not the derailleur. A derailleur is just a device that moves the chain right or left to match the cable input from the lever. Dura Ace has its own quirks, but you are talking 105 so no problem.

Be really careful setting the stops on the rear derailleur. Instant disaster could result if you pull it into the wheel.

exactly what I was thinking.
Anybody know the seat tube diameter. I used a ruler but it looked like 33mm? I'm gonna guess 31.8mm but I don't like to guess. I could try to clamp my road bike stem and see if it fits.

Ooh, yeah. Forgot about that; I made that mistake the other day.
Do it before a test ride, because telling yourself "No worries, I'll be stringent with the lever" only works for me as far as the first stop sign.