When the air conditioning compressor does not engage

Check the climate control fuses, in this order:

an inline fuse behind the console right "cheek panel", clipped to the right side of the main climate control case
the #16 fuse in the aux fuse panel
the #6 fuse in the main fuse panel
the amplifier fuse, inline on the amplifier ground wire, behind the console left cheek panel

The #1 fuse above is the most likely culprit of the four.

If you have original Lucas fuses, bear in mind that they can look OK but the wire can be broken under the caps, so replacement is the best bet unless you have a test light or meter to verify continuity. Clean the fuse clips as well.