Okay this is how my low pressure cycling switch is hooked up in my 04 Chevy Blazer with a p59 PCM. Put the green wire from the cycling switch to pin 55 other red / green PCM connector and the black with white stripe to ground that will let the PCM control the AC cycling. Then go in to your tune for your vehicle go to system click on AC and set type filter to serial cycling. That's how mine is setup up in my 04 Blazer and my AC cycling works. The only real difference I know between the PCM you're using and the PCM that I'm using that mine can do drive-by-wire yours can't.
Just looked at your AC wiring schematic for your 1988 it looks like your high pressure switch and cycling switch are series together to turn on the compressor relay. To make it work with the newer PCM some rewiring needs to happen. You can clone the S10 AC wiring in your setup and make your AC system work correctly it's pretty simple.
1988 Chevy C1500 A/C wiring
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04 S10 Blazer A/C wiring
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