I actually have been doing some real research on Jimmy's gold LED watch, and I believe I've found out what it was.
Here are a few more images of the watch that are pretty helpful:
We can see the approximate shape of the watch in these images, and and I think they rule out the Pulsar line of watches.
Next, here are some nice images of the band/clasp, a real nugget of a clue:
The logo on the clasp is the logo for the Mercury Time New York company.
And here we can see what I believe to be the actual watch used:
Notice first, the case shape, and the "H" shaped links on the bracelet, as well as the placement of the button at 1 o'clock.
I recently got my hands on one of these watches in alright physical condition, but the LED module is cracked in half and has some battery acid corrosion. Unfortunately I don't think it will ever work again, and sourcing a new module doesn't seem likely.
There are no model #'s or any other identification markings besides the metal composition and company name on the caseback. I believe the watch is from somewhere in the 70's.
I'll get some pictures of the one I snagged after work.
EDIT
I actually think there are two different Mercury LED watches used in BCS, and in some scenes, most notably the scene where he enters jail and places his belongings in the plastic bag, he wears a similar Mercury watch with hooded lugs and a more barrel shaped watch, although I haven't been able to get a good capture of that one.