Open the microwave door. Does the light come on? If not, the clock has a battery. If yes, perhaps your TT has a mysterious source of perpetual AC power? Patent it. We all want some...
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2012 Chev Traverse LT with TP