Sounds like the Sunpro may have a lit dial using the third wire. Could be something else---electric tachometer dial maybe---as I've not used a Sunpro device.
Just went back and reread your post and noticed "LCD". You need the directions for your meter and / or call Sunpro TechRep.
I've run across some LCD applications in other uses that require a constant power input in addition to the 'switched' application. If this turns out to be the case, you need the---I think---12-vdc 'running' to your ignition and the 12-vdc 'constant' to the battery positive.
If this starts getting overly squirrelly, consider going back to a basic mechanical readout hourmeter with two wires.
If--and this is an if--the LCD requires constant power in addition to the switched side, and if the machine sits, you MIGHT notice a slight battery charge degradation over time: even a couple milliamps will gradually pull a battery down over time.
Can't overemphasize finding the directions or getting Sunpro tech help. Some LCD devices are fairly sensitive to misapplication of voltage.
I'd wire it where the 'constant 12-vdc' feeds the meter off a switched ignition circuit----key 'on', meter 'on'.
Then, assuming you have a lit dial, run the 'switched 12-vdc' to the headlight circuit 'on' when you turn the headlights on. Or ignore it as relatively unimportant. Note above concerning possible 'constant' voltage for LCD.
Others may disagree but I'm inclined to fuse every auxiliary circuit. Seal all your wire splices to prevent corrosion and failure.
For certainty, run the ground all the way back to the battery negative.
Please post back and advise your experiences so we may all learn.