Japanese cars, compared to European or American ones, often feature through-vane or scroll type of ac pumps, which are rotary pumps, not reciprocating ones. They are supposed to be quieter than reciprocating pumps.
These rotary pumps are fixed displacement so they're supposed to cycle their clutch. However, compared to most reciprocating ac compressors, they nearly always feature a thermal protection switch in series with the clutch coil, which is supposed to trigger and cut power to the clutch coil once the compressor's metal shell reaches a critical temperature (this is meant to avoid compressor damage, i.e. seizure, due to both low oil circulation rate across the system and abnormal superheat, conditions determined by running the AC system on a low refrigerant charge, though not low enough to trigger the low pressure switch/sensor, or not enough lubricant oil in the system or a wrong viscosity one).
Unfortunately, these switches, as with any other compressor part, are subject to wear due to thermal cycling, and the wear may make them start tripping too earlier when old and making the compressor cycle too much, or just stop doing their job.
Your case, if you managed to successfully rule out a clutch gap issue, a condenser fan malfunction, a condenser airflow issue (check for the radiator-condenser gap and replace the insulating foam if it's damaged or missing), low charge, a system leak, a relay fault, a pressure switches or evaporator temperature sensor, or a system obstruction which manages to trigger the high pressure switch/sensor, might be this.
Thankfully, the thermal protection switch on the compressor can be replaced, but if the compressor is old enough and has seen enough abuse (and not running the system for a long long time and then turning it on out of the blue unfortunately is; please tell me that you've at least had the system checked for leaks and, if no leaks found, then the refrigerant levels restored), a new compressor, along with a system flush, a new liquid receiver/accumulator and a proper oil balancing procedure with the oil type and quantity recommended on the compressor's label, might be the best way of dealing with the problem.
What may go wrong having the compressor engaging/disengaging very very frequently?
The clutch assembly (and, in particular, the friction pads) wears faster. In addition the excessive friction heat due to the repeated engagements might damage the compressor's shaft seal.
