Are you sure you want to do this?
If the fan snuffs out the flame, you don't want the gas staying on or kaboom will happen.
If the fan is on before the burner is lit, it may never light up and kaboom will happen.
You have to make sure your burner and controller can deal with a flame out, that there is flame detection sensor in the oven. Electronic controllers have this safety built in.
Convection oven fan I think is an ordinary shaded-pole motor with high temperature oil in the bearings, and a long shaft with a second (inside) fan for the motor. They get pretty hot.
The patent says the fan in a convection gas oven causes carbon monoxide to spike until the oven metal is warmed up, after several minutes.