Is there a hidden buttons combination/sequence for park/neutral?

Hmmm... maybe I spaced out on that one. For some reason, I'd convinced myself from the wording in the first post that it was a two position on-on switch (no central off position,) in which case my solution would work. I meant to double check that, but then I forgot and just proceeded with my schematic. Oops!

Yeah, obviously if it needs a neutral position, my circuit above won't work! Maybe I'll take another crack at my original up-down counter idea. It's fun trying to figure this stuff out... and I've got more free time than normal thanks to the virus.

 

Original Config:
Fwd/Rev switch on cart is a simple on/on spst switch, i.e. 2 hots and a common.

An spst switch would provide only an On/Off function; not an On/On function. Can you confirm whether the original switch has a centre-Off position or not?