DIAGNOSIS: Cooktop light failure. Either the halogen bulb is burned out or the socket/switch has an issue.
FIX: Replace the bulb first. Unplug the microwave. The bulb is accessible from below by turning the small bulb cover counterclockwise. Use a halogen bulb of the exact same wattage and base type (likely a G9 base). This fixes it 95% of the time.
IF THAT DIDN'T WORK: The issue could be the light switch on the control panel or the wiring to the socket. The switch is part of the membrane touchpad or control panel assembly, which would require a more involved replacement.
HEADS UP: Never touch a halogen bulb with bare fingers. Oils from your skin can create hot spots on the glass and cause premature failure. Use a cloth or gloves during installation.