Carey, yes, grounding the wire that goes from the temp sender to the dash will turn on the light.
When the electrical system is working normally, you can test the warning light by sliding up the connector at the sensor to expose the sensor output, then touch a grounded wire there. If everything is ok this will turn on the dash light. Trkrd, you might look for spots where the temp wire is shorted to ground. I think this is more likely than a stuck-on sensor. If possible, disconnect that wire at *both* ends and temporarily replace it with a good wire. If the light is now off, that confirmed a grounded sensor wire.
I won't run it anymore until this is remedied. No Yanny dealers around me. Are there any sending units that cross reference with this one that I might be able to get at a local auto parts store?? ...don't want to wait for the part to come in the mail.
It can't overheat that fast! Don't be afraid to start it up. If everything is normal and considering this cold weather you should be able to touch the top of the radiator tank, and the midpoint of the block, with your bare hand to judge temperature.
If it really is the sensor (and I think that is the least likely cause), pull the sender and take it to NAPA, Autozone, etc and match by eye. In several cases Yanmar spec'ed peripheral parts the same as whatever Datsun (Nissan) was using at the time. This is one reason these old Yanmars are so easily supported, worldwide, 30 years later!
I recently replaced my oil pressure sender with generic, see this thread:
Low oil pressure? No, bad sender!
Since the temp sender is essentially a boilover-anticipation warning, any 70's Japanese car that also used a 13 psi radiator cap should have a similar sender. You just need to match threads and electrical connector. Match to a vehicle with a lower radiator cap pressure if you want a safety margin. (Boilover temp is proportional to system pressure).
If you try this, please writeup your experiment to share with us!
And - everyone who posts here that just bought a Yanmar, wants to put gauges on it immediately. In my opinion you don't need them. I have come to appreciate that Yanmar got it right on a lot of details. All you need is boilover warning and no-oil-pressure warning. Adding on complexity just adds potential problem points.
You will never see a boilover if you keep the radiator fins clean and the cooling system is up to spec. it is designed and marketed to run at full rated hp load, flat out, for the several hours that tank of fuel lasts. That's what the hp rating means! If it runs hot you need cooling system refurbishing, not a more precise gauge.
Harbor Freight's little remote temperature sensor is often on sale for $10 or less. It is a precise way to measure temperature at the block, head, top vs bottom of the radiator, etc. In my opinion that is the diagnostic tool needed rather than a dash gauge.