new BIRKS LED module fitment to other watches

hi all about 7 years ago i bought a birks led watch along with the new old stck birks i got a new old stock module. the module has been in the box for 7 years a shame really . i was hoping you could tell me what other watches these module would fit in to . so i can look for a nice case so i can get the good of the module. the module is 29mm by 4mm deap . the buttons are at 1 oclock and 4 oclock on the right side of watch. any help would be great

this is the watch the new module fits