Nice one.
My two "Big Qs" have their dates of manufacture stamped into the floor of the battery compartment, consisting of 3 numbers. The first two are the year and the third is the month, e.g. 827 = July 1987. Mind you, mine were assembled in Taiwan, so may have a completely different dating system from yours.
According to Timex, these things run on their M135 movement although as one is a date model and one ain't, I'm taking that with a generous pinch of salt. Whatever, here's images of the non-date one.
Regards.