First thing to do is get a set of gauges and check the refrigerant pressures on the low and high side to see if you are low on refrigerant.

You should be seeing ~35psi on the low and ~150psi on the high side for R134 (a little less for R12 which is what your model year originally was charged with - pressures observed will depend on the ambient temperature) on a fully charged system when the engine is running. If it is substantially lower on both sides, you need to add R134/R12 in incremental amounts until the pressures approach these levels, whatever is in your system. An auto shop should be able to do this if you are unsure how to check the levels and/or recharge.

Sounds like you are low on refrigerant to the point where the compressor cycling switch is not engaging the compressor clutch. If this is the original a/c system, there are several places where refrigerant can leak out - o-rings, compression fittings, compressor seal, evaporator and/or condenser. A leak test and or repairs is the ideal solution but can get expensive on an older car.

Or you could have a bad cycling switch - that is why checking the refrigerant level is helpful - if it is fully charged, then you have a faulty switch or failing clutch on the compressor.