[JollyElm]

Can you tell us who all of the other autographees (is that a word?) on it are?

Rightly or wrongly, the base assumption is that this was signed by team members during Frank Robinson's tenure as Giants manager from 1981 to 1984. If the other signatures fall in line with that timeline, then there are only a few Jims (watch, it's going to turn out NOT to be someone named Jim) it could be:
Jim Wohlford
Jim Barr
Jim Lefebvre
Jim Davenport

The first letter of the last name could possibly be a 'W' or a flamboyant 'D,' so it's a tough call without having multiple examples of the players' autographs to compare it to. Both Wohlford and Davenport also have a single descender ('f' and 'p' respectively) in almost the same part of their last names, so that makes it even trickier.

Edited to add: The Willie McCovey signature may sink my theory, as he was no longer part of the team, but his is in a different ink, so there's a good chance it came later.