Welcome Wristie:
Your unit was built before the advent of R-134A and probably has R-12 in it. I lean toward a defective high pressure limit switch or a kink in a refrigerant line. The problem is called 'short-cycling' and is normally caused by high head pressure (the compressor can only pump up a certain pressure and must shut off to allow the refrigerant to equalize pressures on both sides, then try again).
Glenn
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