Gas oven electric igniter?

Is the igniter in a gas oven (Maytag) supposed to turn off after the oven ignites or stay on glowing orange the whole time the oven is cooking? Our oven is giving off horrible smells recently so when I cleaned it today I fired it up with the burner cover off and found the igniter smells when it comes on but it stays on the whole time the oven is on even after the burner lights. Everything else has been cleaned even the burner and air shutter. But I think the nasty smell is the igniter.