I wonder if it is a bad switch or a loose wire connection.
You can use a 12V light bulb to verify you have power to the switch if you do not have a multi meter. You should be able to jumper across the switch to verify if the switch is good/bad, once yo know if you have power up to the switch.
Not sure your TT configuration, but my microwave is above the stove hood. A few years back, I removed the microwave, and noticed I could access the wires connections for the stove hood from that cubby.
2012 Jayco X23B
2020 Ram Laramie 3500 SRW Air ride 50Gal fuel tank.
2007 Dodge Dakota Quad Cab (retired from towing)
Equal-I-zer 4-Point Sway Control