Your thoughts on Omega watches made for Olympic games

My read is the serial number is for 1927/1928.

6.7 million. So my guess is the enamel with the 36 Olympics is modern and added recently considering the condition and what appears to be a normal pattern behind it.

As for price as a 1927-28 pocket watch, and if you can remove the modern enamel glued on? Not sure but you can google 35.5L -T1 movement which I think refers to a 35.5 linge/line movement. Or something along those lines with a 14k gold case.