Welcome to JUST ANSWER small engines, let me try to help you !!
# XXXXX is spring that should pull the # XXXXX bracket into place to hold the brake when applied. Is this spring in place?
Only adjustment on the brake is the rod # XXXXX going back to the brake lever on the transmission. This should have nothing to do with parking brake latch.
Looking at the schematic, the spring appears to be there, connected and okay. The knob (#17) appears to hold for a second in the up position and then releases. There is a plastic guide at the top of #16 rod that I don't see in the schematic. I'll have to double check the mechanism but any other thoughts? Twisted #16? Plastic guide at top of #16 rod too high or too low?
The latch has to meet the rod, it can be bent.??
The rod moves up when the knob is lifted. I'll need to look at it some more
OK> Let me know.