Bryant AC was turning on and off intermittently (1988). Does Carrier/Bryant have a vapor pressure switch that causes this?
Its called a suction line low pressure switch and yes any brand can have one especially higher end units. They are a normally closed switch that opens on pressure decrease and automatically closes on pressure rise
So during operation and unit turning on and off, is this normal?
It’s normal, but not supposed to be…
Low refrigerant charge, restriction, clogged filter dryer, kinked refrigerant line, bad pressure switch, 1lb of solder at a soldered fitting…
Did the compressor shut off, or was it just the fan?
If it’s just the fan, that would be normal and O.K.
HVAC is just so simple… :-0
It most likely does have a VPS (vapor pressure switch) in addition to the LPS mentioned before and of course an HPS.
A tripped VPS will just shut off the exterior fan and a tripped LPS, HPS or DTS (discharge temperature switch) will shut off the compressor and fan both.
In general, compressor short cycling (less than about 5 minutes between starts) is very hard on the compressor.
The compressor has been working to raise the discharge pressure and lower the suction pressure. When it stops, that difference in pressure needs some time to equalize through the expansion device before it starts again. The compressor is not designed with enough torque to overcome the large compression ratio and you can damage or destroy the motor windings.
Compressor short cycling for any reason is a defect.