The compressor relay location on a 2003 Lincoln Navigator is
in the Power Distribution Box (PDB), also known as the underhood fuse box. It's not always clearly labeled as "AC Compressor Relay," so you'll need to consult your owner's manual or a wiring diagram specific to your vehicle's year and trim level. The diagram will show the relay's location within the PDB and often provide a description to identify it.
Look for a relay that's associated with the A/C system. It might be near other relays related to the blower motor or other electrical components of the climate control system. The relays are usually easily removable and interchangeable-looking, so using a wiring diagram is strongly recommended to avoid accidentally replacing the wrong one.