It sounds like your Jeep's previous owner did not get the TIPM recall done. Here is a link to a thread about the TIPM Recall
T. Many of the symptoms you are reporting are similar to those experienced by owners of vehicles with defective TIPMs.
Best bet would be to take the vehicle to a Jeep dealership and have them check to see if this recall has been performed on your vehicle or not. Even though your vehicle is no longer covered by the original warranty, the recall would be performed at no cost to you if it has not been performed before. It's a simple task for the dealership to know whether or not it has been performed or not simply by entering your VIN in the system. Be sure to tell them you are asking about this because you are experiencing problems specifically addressed in this recall.
If the recall had been performed in the past and your vehicle is still experiencing the problems the external fuel pump relay installation is supposed to alleviate, the dealer should work with you and FCA for a solution since as you will see in the referenced thread, sometimes the "fix" doesn't fix anything.
Let us know how your visit with the dealership goes.