When it comes to the ''4WD!'' Warning light that comes on, there's a few places to check.
1: inside the drivers side front, you have to remove the plastic trim piece that the door closes over + the kick plate where the Hood Opener Latch is. Once you have these 2 pieces removed & all the wiring is showing, look for the ''4'' Pink Wires. That Pigtail connects to 1 Pink Wire. Make sure there's no corrosion there. Snip the corroded ends off, then connect all the clean ends back together again.
2: If that was okay, or still didn't correct the problem, I have been told that the 4WD on/off Lever assembly on the center floor console could be bad or corroded, which can trigger that 4WD! Light to come on. If that looks good, or you know for certain you haven't spilled liquids on the assembly, check #3. (Note that if you have to remove that 4WD assemble, check on YouTube for the ''Center Floor Console removal''Video.)
3: Under the hood there's the Fuse Block (Box) aka the TIPM. The number 2 fuse on my 2010 Patriot is for the 4WD/4WD!. Sometimes the wire in the harness that goes to that fuse can also have a corroded end, inside the harness plug, which will kick the 4WD! warning light on. Although you may need to unplug the harness's to the TIPM/Fuse Box so you can look at the wires that go into that plug. On my Patriot, it's the ''Red Wire with a White Stripe''. That wire may either have a corroded end, or in some cases because of the ''thin & cheap'' wiring used, it may have a break inside the insulation. I watched a YouTube Video where the guy found a bad spot in the wire about 1-foot from the TIPM/Fuse Box. He spliced his and got the light to stay off.
4: On the Compass & Patriot, there are 3 Ground Pigtails, 2 that bolt onto the front clip on the drivers side & the 3rd connects to the body along the front side where the engine pulleys are. I have found wires corroded where they fell out of the Pigtail Connector. Although that didn't correct the 4WD! issue, it did correct the issue I had with the ''Right Headlight'' not working & the ''Brake Light'' coming on usually 3-5 times, everything I would start the vehicle and drive.
If you have went through all these steps, find a reputable repair shop that have electrical experience and who also have one of the Scanners. Forget going to AutoZone & have them scan your system, you want someone with one of the $4,000-$15,000 Scanners.
That is my next step. Although working on all 3 of those Ground Pigtails & reconnecting them to the vehicle seemed to make my jeep run better, plus fixed a couple of electrical issues, all that is left is this damn 4WD! Warning Light that comes on anywhere from when I start it and drive 1/2 mile to 2.2 miles (which has been the longest it stayed off.)
My last Note to you is this. I hit a bad chuckhole this summer & that light went out, which leads me to think that there's a connection issue somewhere but let me tell ya, these vehicle electronics are so complicated, you really need to know your way around the electrical system. That's why I am taking it to a repair shop I've dealt with before & have them scan it and if necessary, have them repair it. (Unless they tell me it's the TIPM/Fuse Box) Because you can order a refurbished one which will require you to ship yours back to them because there's a ''Core Charge'' on the unit. Forget getting one from a salvage yard. These TIPM's have 3 or 4 PCB's inside which could have all types of the usual issues, plus the unit needs to be programed to your vehicle. The place I found online charges like $300 to $400 for the unit, whereas a Dealership or Garage will charge anywhere from $800 to $1,300, just to do a 20 to 30 minute job.
Good Luck and be sure to reply to how you got you vehicle fixed so I can pass it on to other forums.... Dan