If you look infront of the oil refill port on top of the engine, there is a
temperature sensor used by the vehicles brain. Behind that is a round
sensor with two spade lugs. The large one to the front is the temperature
send signal which goes directly to the temperature gauge. The smaller one
to the rear is the "engine has reached critical temperature point"
ie. it illuminates the overheat indicator at the top of the temperature
You need to know whether your guage is okay. The easiest way to check this is to briefly short the temperature send signal lug to earth and see if the needle goes to the far end of the hot range of your gauge. If it does, the guage is good and the sensor needs changing. If so, check the resistance of the sensor relative to earth. It should be from memory about 140 ohms cold to around 50 ohms hot give or take.
To check the wiring, you need to check the continuity between the temperature send signal lug, and the respective point it enters on the LHS cabling entry on rear of instrument cluster. Whilst there, again, short the temperature send signal (except at the instrument cluster end), briefly to ground and see if the needle goes to the hot end of the gauge. If so, a wiring problem, if not, the gauge needs repairing or replacing. I have repaired the gauges before although it is very fiddly work. Quite often, one of the fine inductor wires severs close to the solder post end and it can be fixed with a careful steady hand.