The fault light comes on when using propane IF: It doesn't light/3 trys and 'locks out' OR if the ECO (high temp t-stat has opened 180*F)
The fault light will come on when using electric IF: ECO has opened.
Common between gas & electric....ECO
The normal t-stat is not opening all the time so the ECO is opening shutting down the WH.
Normal t-stat may not be making good tight contact with tank wall....or area under t-stat is corroded.
Loose connections would just interrupt DC power and WH would stop working but you would not get a fault light.
Get a new set of t-stats...remove old set....clean contact area on tank wall...install new t-stats