The other sensor is the ecu coolant temp sensor

the ecu then manages the fans, which as a backup have their own thermoswitch in the radiator. This too can fail, but the ecu should still trigger the fans if the block starts to cook...
Any doubts about either then replace both sensors. You can also follow the fan test guide to be sure that they are working as they should.
In your example I would start with the fan test, then replace the gauge sensor if the fans check out fine. Any further issues then change the ecu sensor

Obviously for ease of access vs cost, you might as well replace both. And unlike crank and cam sensors, pattern sensors from reputable local motorfactors are usually reliable. Not sure how much genuine gm sensors are, but when it failed on mine, the genuine ecu coolant temp sensor was in stock and about £12 iirc

Generally speaking, if the coolant has been changed regularly from new with the correct mix then the sensors should be pretty bombproof
