@slowboy , Keith, Temperature gauge is acting screwy and fuel gage fault may not even be the BCM. Gm was notorious for fuel gage issues some were because of faulty sending units in the tank and some had faulty stepper motors for both the Temp. and fuel gage. Also if any air in the cooling system can make the temp gage act very erratic. I suggest you look at the TSB 1st link below. As far as repairing a module, with out proper equipment to test may not be possible asside from checking and cleaning connections. May be possible to install a good used part from same type of vehicle with same options. 2nd link is forum that also discusses issue. Good luck. I hope this helped you out, if so let me know by pressing the helpful button.
http://www.revbase.com/BBBMotor/TSb/DownloadPdf?id=171097
http://aztekfanclub.com/service-related-issuesrepairs/bcm-replacement-with-pictures/