I had movement like that when I got my 336. There are two bolts which face upwards in front of the center pivot which, when loosened, allow you to adjust the gap a decent amount. It'll depend on how much adjustment has already been made if you can close the gap or not on yours. On mine, it snugged it right up to where there was barely a shimmy left over. I had the same 1/16" gap on mine.
I'm assuming this is the center pivot point, and it moves to the front or back based on which direction you turn the wheel? That is where my gap was.