It turned out we had a faulty pressure switch on ours when it was doing similar to yours but, we never had a low freon situation.
It does sound like a pressure switch problem. In the old days, like over 30 years ago when I worked in a shop, a cycling compressor usually meant either a pressure switch or a low pressure situation.... low of freon.
I believe the switch they ended up replacing on ours was up front under the hood. I think to diagnose it, the tech simply jumped the switch and it stopped cycling. I didn't get to watch him make the repair so I'm not 100% sure.
Good luck
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