Airconditioner will not work

The fuse is in the smart junction block? What is amp rating of fuse? My thought, for testing, use a new wire for proper wire color with inline fuse at sjb to rear lamp. I looked at wiring diagram, appears to be more than one fuse, don't know which one is blowing, the amp rating would help. I can only help with testing.

If the rear ac is blowing cold the the ac system is ok. Is the front inside fan not blowing and that is what you mean?

Ok If it keeps bloowing the fuse it means that its to much resistance in the system. I would reccomend you to take a look at you're blower motor. Even if it work properly it my be durty or to old so it requires more power to spin and then its over heating the wires and the fuse automatically blows up.
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does the fuse keep blowing ?? it is also on the same line as the cigarette lighter if the fuse is blowing check that there is nothing stuck in the lighter socket that is shorting it out. Could also be a bad ground wire not makeinig contact.

Sounds like a vacuum leak. Check the vac supply on the intake manifold. Passenger side front of intake.

check for system leacks (lines,fittingis,comperssor,dryer,condensor )

I'm going to assume that is on both sides of the cab? I'm going to say you have an actuator problem, if it's in fact only blowing cold in the rear, and not in the front. The actuators are prone to problems on the gm product lines. Even more with a weak battery.

check for a problem neutral switch and wires
may find that switch is loose and grounding out the wire connections or plug

check to see if the fan is wired correctly. if the wires are backwards the fan will work but because it is spinning the wrong direction it wont blow the right airflow

passenger side right above the airbox 1 plastic line it loves to pop off