Assuming that you have a single lead temp sender, if you remove the lead from the sender unit and connect it to earth (-) the gauge should go to HOT+++! If it doesn't move it's the gauge, if it does move then its the sender, the earlier ones have the 1/4" / 6.3mm tab riveted on, over the years these work loose or corrode and can play up, I have in the past soldered either a wire direct to the sender or the tab to the sender... Depending on whether it's broke or just loose. Obviously the sender can just fail, but it might just be a loose connection:thumb:
If it's a 2 wire sender then just short them together to test ;-)