The temperature senders installed in the radiator control the relays which in turn control the cooling fans. The temperature senders in the radiator have absolutely nothing to do with the water temperature gauge in the console.
The factory-installed temperature sender in the expansion tank is responsible for the console temperature gauge reading.
Mounting the sender in the expansion tank was not correct and that is why most owners have relocated that sender to the engine block as outlined by Rocky.
It was not correct because a hose failure or other coolant system leak would eventually cause the expansion tank’s sender to not be sensing the water temperature but instead the air in the now empty/low level expansion tank.
If your car has had no previous overheating issues then there is no reason why you should expect any just because you cannot read a current temperature. But it really is quite easy to correctly install the sender where it belongs.
Larry