** The full model number is: 790.96613409. I made a assumption that one smooth top model 790 was like another.
No, just made by the same manufacturer. Every manufacturer makes numerous designs of appliances, comprised of varying components.
** I "think" the read out was: "F31 Err". **
An F31 error code on your model indicates a problem in the oven temperature sensor circuit (see the following link). That could be caused by just a failed oven sensor itself but could also be from a problem in the wiring to it or in the sensing circuit of the electronic control.
** on several occasions it would trigger when we tried to set a Bake function, and would trigger right when we pressed the Bake button itself, and before any associated Temp was selected. **
Such a condition might give you an opportunity to test the sensor itself to see if it might be the cause as described at the link above. Otherwise it is going to be more difficult to pinpoint the cause with any certainty.