Tappan Stove elec/control/timer

They no longer make the elec/control/timer. But that is not the problem I’m having, the button on the unit itself broke off. The buttons are still orderable. My question is, “How do I get the remnant of the button stem out of the unit to replace the button?” Please help me try to fix my stove.

The only thing I could think of would be to try some tweezers or needle nose pliers