If your 2001-2004 Escape has the factory tow package, you should see the wiring harness (13A576, shown below) under the load floor carpet, and you'll have a connector hiding under the left side of the rear bumper cover (C439, shown below).
If the harness is not there, you may still have the wiring already installed internally. Remove the driver-side tail lamp assembly and look around inside the rear body opening for an empty connector (C423, shown below, the side without the arrow). You may find another connector for the power point (if you have a power point). If it's the correct connector for the trailer wiring, it will have only four wires: WHITE, DARK GREEN, YELLOW, and BROWN WITH WHITE STRIPE.
If that connector exists, you can buy the 13A576 harness (part number YL8Z-13A576-AA) for around $15 from any of the on-line Ford parts distributors. You may also need to buy the $40 trailer flasher module (part number YL8Z-13350-BA or Motorcraft SF-621) if the trailer lights do NOT work, even with the new harness installed. This yellow flasher module replaces the blue flasher module under the instrument panel near the hood release.
If you have that connector and don't want to wait for the Ford harness, just connect those wires to the same color wires on an accessory trailer connector (the BROWN WITH WHITE STRIPE wire goes to the BROWN wire on the trailer connector). You may still need to buy the yellow flasher module.
If you don't find the C423 connector inside the rear body opening, you'll need to buy a trailer wiring adapter for cars with separate rear turn signals. If that's what you find, please post back here, and I'll give you the wiring diagrams for it. You'll need to connect four wires on the driver's side, and run one wire from the passenger side.
Whilst on the subject of wiring up towballs, does anybody know how I should wire up the 12V S socket, the one which is used to power the caravan electrics, viz charger, fridge, reverse lights etc??? :shrug: