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The tpms will not naturally be replaced when the tires are replaced. I replaced mine this week with oem schrader I got from Amazon. 45$ each! So I bet the batteries are bad. I could sync the rears but the front would not. They say the sensors are good for about 10 years and so they are probably that old.
The original TPMS part in the '97-2000 Corvette was #10438853 which has been replaced and is now interchangeable with the Schrader #28006. This is the one that has been recommended here on the Forum for a while now. They're available from Rock Auto.for $25 @. https://www.rockauto.com/en/parts/sc...)+sensor,12036
Forum Member bc6152 bought this one from Amazon... and says it fits around the valve stem on his wheels.
I have a similar magnet I removed from an old car speaker, but I have the C5 Z06 wheels and because of the ribs in the wheel had trouble getting it close enough to the TPMS. I used a couple of smaller magnets I could get closer to the valve stem.