What year, and if a 66, what month?
I've have little problems with the half dozen 65-66 Fastbacks I've owned. Sometimes I wish mine wouldn't, it's a pain to unlatch it sometimes. There are "adjustments", the folding seat hinge goes up/down (shims) and back/forward for one (bolts under the fixed section). The latch itself (two different types in 66) has some minor play in it too.
Jim
I see yours is a early 65. There is a stop on the latch that may be the problem as well as the two brackets on the fixed section. Look at the latch with the seat "latched" and determine which direction the seat needs to move.