Download the 2003 Jeep KJ Service Manuals as per LibertyTC's link.
The Fan Relay on the 2003 3.7 gasser is an externally mounted Solid State Relay.
This relay is a variable relay ie. unlike a normal mechanical relay as you will find in the Fuse Box under the hood or on the interior fuse...this Solid State Relay is "pulsed" ON/OFF by the PCM to slow down or speed up the fan. This Relay is bolted near the Fan in the engine bay....will have four wires going to it....Dark Blue/Pink, Yellow, Light Green and Black with Orange Stripe. This Black/Orange Stripe wire goes direct to ground so I would splice a wire onto this wire and ground it to Engine/Chassis somewhere nearby.
The 2003 KJ I believe is the only KJ to use this type of relay and they are known to cause problems which is probably why it got dropped in later KJ models!
So you could try find a new one or one at a Breaker Yard from a 2003 KJ!
The Component Location in the Wiring Diagram Section 8W is supposed to direct you to the relevant Circuit Diagrams for this Radiator Fan Relay but Jeep decided to rather make this into a Treasure Hunt!
So the relevant pages you need are 8W-30-23, 8W-15-5, 8W-80-85/86/7.
If you cannot simply replace the relay...it will be pretty hard to track down a problem in the wiring!
So in this case I would suggest that you fit a small ON/OFF switch inside the cabin that interrupts Fuse #2 40 Amp inside the PDC under the Hood ie. cut off the Dark Blue/Pink wire as shown on 8W-30-23 and fit your switch into the cut-off section.
This way you can stop the fan from clicking ON/OFF when you turn off the ignition but do not forget to switch it back on when you drive off....assuming the Fan does actually switch ON/OFF while you are driving.
If the Radiator Fan Relay is Faulty I think that the fan will either not run at all or will run as soon as engine is running!