I checked ALLDATA. The A/C switch grounds the AC SELECT input at the Powertarain Control Module (PCM). The high (normally closed) and low (normally open) pressure switches in series (may be the same housing) ground the AC REQUEST input at the PCM.
With those two inputs, the PCM sinks the AC RELAY output. This should engage the AC compressor clutch. I am also assuming that it sinks the FAN RELAY output for the radiator fan relay, unless it's already on based on the ECT (engine coolant temperature) input.
(The single fan only has one relay and one speed, near as I can tell.)
So cold, fresh start, the A/C is off, and the high and low side A/C pressures are equal... enough pressure to close the "low" switch and provide the AC REQUEST signal.
However, as soon as the AC compressor clutch engages, the compressor "pump" tries to move low side refrigerant to the high side, raising the high side pressure and lowering the low side pressure. That's the way it's supposed to work. But if the system is lacking refrigerant, the low side pressure becomes TOO low, and opens the low pressure switch, defeating the PCM AC REQUEST signal.
The PCM rightfully determines this is a problem, and disables the compressor clutch and fan relay. Then, the low and high side pressures equalize, the low pressure switch closes, and the PCM tries again to engage the AC compressor clutch and radiator/condenser fan.
The PCM doesn't know the actual pressures, or the state of refrigerant charge, so the whole cycle wickedly repeats.
@Monie, you need not be concerned about any of this technobabble. Get your AC refrigerant charge checked by a professional with the proper manifold gauge set. It is quite possible a 20-year-old vehicle has developed a small leak, perhaps at the compressor shaft seal, and is missing some needed refrigerant. Your system can be leak tested and recharged for a complete and proper repair. I would not suggest simply adding a can of refrigerant from the auto parts store without thorough knowledge, a leak test, and the proper gauge set and equipment.