A/C compressor cycling rate is a function of charge state, cabin temperature and ambient temperature. In an individual event, if the pressure falls below a certain amount (around 25 PSI on the low side) a low side cutout switch turns off the clutch and the compressor stops. In the "off position" the high side bleeds into the low side, increasing its pressure. At around 45 psi or so the switch kicks back in and the compressor starts again. How often this happens depends on the first things I mentioned.
This was not some "engineered" event, it is just how the system has always worked on a "fixed orifice" system. The refrigerant used is secondary. You may in fact have a bad low pressure cutout switch, or a significant overcharge.
When you converted, did you evacuate and put a measured amount of r-134a in the system? Remember the amount of r-134 should be about 80-90% of the previous amount of r-12. Put some gauges on it. Watch the low side pressures as it operates.
Otherwise it may likely be a bad switch.
HTH.