Originally Posted by willwren
Even if your recovery tank is full, it doesn't necessarily mean the radiator is. Check your radiator level, and if it'* fine, either disconnect or replace the level sensor in the radiator. It may simply need to be removed and cleaned (both the face of the sensor in contact with the coolant and the electrical contacts).
I'm going to vote for a flaky sensor here; mine goes off routinely for no apparent reason. I'd love to know how to clean the contacts, but there doesn't seem to be any moving parts to this sensor and the little metal pins that stick into the coolant don't seem to be dirty or corroded, so...? Maybe it'* just been cooked too much over the years and its internal resistance has gone wrong, leading to a bogus Low Coolant signal. I haven't been able to find anything in the service manual about what its resistance is supposed to be in the first place; I imagine GM would just say to replace the thing if it gives false alarms.
You can simply unplug the wiring harness at the sensor to get the alarm to shut up, but then you'll probably forget to ever get around to fixing the sensor after that, and I can tell you from experience with our Trans Sport that it is a Good Thing to have that sensor working for you.
P.*. Have a rag handy to stuff in the hole if you remove the sensor for testing or replacement, since obviously your coolant is going to all come running out when you remove it...