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What I understand is that in later years the A/C control was moved to the BCM and as such you are unable to control the A/C activation with the PCM. You need a pre-2003 PCM to do that.https://www.lsenginediy.com/upgrading-gen-iii-ls-series-pcm-air-conditioning-guide/
I have a Vintage Air, Gen4 system in my 81 K10 and the system is self contained. Just supply the power.