Healey Z:
If its the original guage, its the mechanical gas type utilizing a bordon tube behind the face plate. Most common failure is a leak in the tube or bulb, allowing the gas to escape. You can remove it and send out to a repair shop, or buy a new one which is close to original.
If its an aftermarket, electrical type then its a different animal. Start by checking for power at the guage, then the resistance of the sending unit to ground at temperature. That will tell if its the guage or the sending unit.
Let us know how you fare?
Jerry Rude
BJ8
Lotus Europa TCS 'Guenhwyvar'