Instructions
Take your watch to an antique dealer or an antique jeweler that has knowledge of Disney collectibles.However, if you cannot find one with prior Disney knowledge, that is OK. Most dealers will have access to product catalogues, or they can put you in touch with someone who does know. If the watch still has a serial number, they can use it to trace the production date. If not, they can use similar traits and characteristics of your watch to compare with others.
Another option is to check on Ebay. Many Disney collectors will list products for sale. You can check to see what prices the watches are being auctioned for. Products are divided into collectibles before 1968 and collectibles after 1968.
Check in books/collectible guides like The Official Price Guide to Disney Collectibles. This guide comes in two editions, which cover more than 28,000 Disney collectibles. They can be purchased online.
Bayvender Collectible and Character Watches is a site that carries hundreds of vintage Disney watches. You can scroll through their collection to find your watch, and its production date.