Cat 3406b high temp

I was wondering if anyone could help me diagnose a high temp warning light issue. The light and buzzer on my 3406b has come on a couple times however my fan did not kick in. I swapped this motor into a new truck and I took the temp gauge from the truck the motor came out of. The gauge only reads 200f when light and buzzer comes on, fan used to kick in around 205f when this motor was in the old truck. I’ve replaced the single wire sensor for the temp warning as well. My question is how can I narrow down if my buzzer is coming on early, or if the gauge is reading low? The sensor for the buzzer that I replaced is rated for 215f so there is definitely some kind of discrepancy.

Thanks in Advance!