Rooftop AC Cycles on and off and lights at same time

I have a 2005 cougar 5'er that had the same AC trouble. It was the thermostat
that was clicking off and on.
The lights were dimming from the AC drawing so much current trying to start so many times, too close together, from shutting off then turning on under a load so many times too quickly.
The start capacitor in the AC was working overtime trying to keep up with the "stat. cycling on and off with just a one or two degree change.
Change the cheapie thermostat out to a better unit.