I have replaced the clutch hub twice on 5.0 Mustangs and it has been an effective fix when the hub failed. If the elecromagnet coil is functioning properly,and the clutch does not engage and turn the compressor, then the hub is the problem.
The A/C clutch is about $100 new or you can buy a compressor from the junkyard with a working clutch for about $50. The puller is about $16 if you have to buy one, Autozone will rent you one for free.
The clutch hub is usually what fails, the rubber shock damper shears off from the steel hub and plate. The pulley turns, but the hub doesn't when you power up the A/C The hub comes off without much problem if you have the puller. You don’t have to do anything with the refrigerant (R12 or R134a), you can replace the clutch without draining and refilling the system. The snap ring hiding inside the hub is the only tricky part.
A few simple electrical tests are advised before popping out the wallet to buy a clutch assembly. With the engine running, use a test light connected to the 2 wires on the A/C clutch harness to make sure you have voltage when you turn the A/C on. If the system is low on refrigerant, the clutch will not engage (safety feature, keeps you from burning up the compressor due to no oil). There is an aluminum canister on the firewall with a large hose leading to the A/C compressor. There is a pressure switch on it with a 2 wire connector: pull the connector off and jumper the wires. The compressor circuit will power up, and the test light will light if the electrical circuit is good. This test is also a good way to check the compressor & clutch if the system is low on refrigerant. You can jumper the wires and the compressor will turn if the clutch is good.
The clutch also has a relay that shuts off when you go to WOT (wide open throttle). It is located on the passenger side inner fender well. The close proximity of the relay to the headers can cause the insulation on the wiring and the relay socket to deteriorate. The relay can become non functional when this happens.
Diagram courtesy of Tmoss & Stang&2birds
See the following website for some help from Tmoss (diagram designer) & Stang&2Birds (website host) for help on 88-95 wiring
Mustang FAQ - Wiring & Engine Info Everyone should bookmark this site.
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http://www.veryuseful.com/mustang/tech/engine/images/IgnitionSwitchWiring.gif
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http://www.veryuseful.com/mustang/tech/engine/images/88-91_5.0_EEC_Wiring_Diagram.gif
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http://www.veryuseful.com/mustang/tech/engine/images/TFI_5.0_comparison.gif
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http://www.veryuseful.com/mustang/tech/engine/images/MustangFuseBox.gif