-If you're sure it's a Red Sox cap, looks like some of your sigs have a number so start here:
https://www.baseball-reference.com/teams/BOS/uniform-numbers.shtml
-It's a listing of all Red Sox players by number...say you've got #14 & it looks like the last name begins with "G"....go down to #14 & see which Red Sox players wore 14. Do an image search for signatures of the likelies.
-Once you get one match...you'll be able to check when that guy played & narrow down the years you're probably looking for (unless everybody signed at an oldtimer's game or something & the signatures are from different eras).
-Hope this helps...or a Sox fan with a photographic memory for sigs happens to see this, ha-ha!
