A/C Grunts once and won't start

What's the Make and Model?

Assuming it has one fan motor, it'll have Run Capacitors for Fan and Compressor. Total of two Run Cap's. They're called Run, but the motors won't start without one or with a failed one. They may be separate or in a common case.

It may (probably does...) have a Start Assist made up of another capacitor and some form of switching device.

If you can get up there and take pix of Manufacturer's Model/Serial/Rating Label, Wiring Diagram, and Capacitors, please do, and please post them.

Haven't detected a pull down on the voltage by the lights dimming. Not at the camper until later in the week. The A/C was used quite a bit during the preceeding week without a problem....just this mistake to try to restart so quickly. It is eight years old, never had any trouble, not even recharge needed.

What is the voltage? How much does voltage sag during the attempted start? How old?

Yes the start capacitor might be shot. Not sure how to test... maybe just replace.

Time to check the capacitors. They are located in a small compartment accessed by removing the roof-top cover and then the electrical compartment cover.