AFAIK, Yanmar neutral safety switches are an optional extra and are always installed on the shift lever. I don't know of any installed in another place. If you do have one, and it is not on the shift lever, then it needs to be someplace that will activate it when you put it in gear. That means it would need to be next to the saildrive shift stub, and there would need to be two of them - one for each direction. These switches are very small microswitches, so I very much doubt it is located on the saildrive because it would be extremely difficult to mount there. Your single
shifter would also require two switches, which would also be difficult to mount. This is why I think you do not have a neutral safety switch.
Again, go to an autoparts store and buy a $6 Bosch-type relay and swap it for your existing start relay. These relays do go bad, and they don't always fail catastrophically. They are cheap
and you should have a spare anyway, so nothing is lost
by trying this. Your starting problems may just be coincidental with getting the shifter into neutral.
If you are convinced that you do have a neutral safety switch in your system, then it must be installed in the starter relay circuit. Go to the relay box on the engine and follow the circuit wire back until you find it. If you don't find a switch, you do not have a switch - there are no central computer or electronic transducers here, it will be a physical switch mounted against something that can activate it.