Yepp, I agree with your post! We don't make watches from scratch, but we do restore watches: we clean movements, can change the odd wheel, can replace a balance wheel, stem/crowns, etc. I think it at least qualifies to "watch restorer".
I have taken several Swiss watches apart, cleaned every part and put them back together again. I know this does not qualify to the title "Watchmaker" ( although I have actually made a few staffs in my shop, but the machinery there are meant for somewhat larger dimensions! ), but maybe "repairer"?
In regards to Timex movements: Even though they appear to be simple and "easy" movements, they are NOT the easiest to disassemble, not to mention REASSEMBLE! Removing the plates is easy enough, but trying to put these back together again requires a steady hand - at least as steady as on any "High Grade" movement - all in my opinion.