Doesn't sound like YOU need to swap the wires over for the temp gauge tbh, when that is the case, the gauge reads the opposite way around. Yours isn't.

Did you turn the heater dial inside the car to heat when you ran the car with the coolant tank cap off?

​​​​​Is the aux belt routed around the water pump pulley correctly?

Thermostat could be stuck?

Are any of the coolant hoses hot?