The overhead outside temp gauge does not read correct on 1999 olds silhouette

SOURCE: where is the outside temp sensor located

You will find the ambient temperature sensor behind the grille and in front of the condensor. The grille will have to be removed to replace the sensor.

SOURCE: torque converter circuit

There is a simple fix... you can unplug it ( a shop can do that in about 1 minute or less.)
It has to be taken apart(transmission) to install a new module.. Unplugging it will get rid of the OVERdrive function.. meaning a little higher RPM at highway speeds.. but will be cheaper than a 1500+$$ job of removal and repair....

SOURCE: Working on a 1999 Oldsmobile

One guess is there is air in the cooling system. The air pockets will cause temporary overheating (fluctuating guage).

It sounds like a bad head gasket is creating these air pockets.

SOURCE: 1999 Oldsmobile Bravada Heating Problem

when engine is cold remove radiator cap and check coolant level,sounds like it is really low and has an air pocket in it.

SOURCE: the fuel gauge on my 1999 oldsmobile silhouette

I had this issue on my 2001 Aurora. The fuel gauge is part of the fuel pump assembly. Replacing the entire unit is expensive. I found a write-up online where a guy showed how to buy just the gauge part and repair it yourself. Took me about and hour and $23.50 in parts.