Becker played for six teams in MLB, but he's only in the Batters Pack as a Twin and a Brewer (the 1990s listings still only being partly complete). Don't know what I can do about his days in Baltimore, Detroit or Oakland, but I can at least help with the Mets.
This is a good picture, but with that damn black cap that Charlie "Memorastealia" Samuels was so fond of (then-Mets equipment manager, later revealed as a thief, whom you practically had to hold down to let the Mets wear their traditional blue caps), it's tough to see against the dark background.
Fortunately, Becker had been something of a prospect coming up with the Twins, so he still appeared on a couple of cards that year, before being squeezed out of the sets entirely in his later years. Here's his Upper Deck card, both unabridged and with the card printing cut away:
Which, with a facial cutdown and a bit of adjustment to deal with the "dramatic" lighting, makes a good mugshot 90x135 image, IMO:
Finally, I found a lovely blowup of Becker's Fleer Ultra card that year, but again the black cap and the angle of the head make it less-easily-identifiable than some may like. Still, I include it for completeness's sake:
