Now That's a Whole ..............
But my hour meter is mounted on the engine compartment wall,
........ different matter.
The wire spare terminals on the engine (as you've mentioned) may offer some help in finding the electrical supply you require.
If I can suggest, with the engine off, use a voltmeter between each wire and ground and make a list of who's live and who's not.
Then, making sure that all of these wires are very easily accessible, start your engine and once again check each wire for power. I won't bore you with the need for safety here

.
If you find a wire that is energized ONLY when the engine runs, you're off to the races. Use #16 wire as your hour meter will have near zero amperage draw.
But as you well know, life's a bi*ch and then you die so don't hold out too much hope for this.
Moving right along, you're next step (assuming this didn't work) is to go into an alarm circuit and install your meter. In my previous post, I went a little overboard and suggested using a solid state relay. Taking a second look at this, you MAY (as in might, possibly, or be really lucky) be able to insert the meter in parallel with the alarm circuitry without activating the audible alarm. I needed a relay as I was looking for 3A.
Looking at the attached diagram (better still, see post #6 below), I am hoping that your hour meter has such a high resistance that the new wiring for the meter DOES NOT offer an alternate route for the electricity to flow to ground and activate the audible alarm. I'd suggest a pocket full of cheap alligator clip wires and try this out to make sure the meter does not conduct enough electricity to sound the alarm.
Send me a PM if you need any further guesstimation on this.