Fuel pump relay bypass?

I don't see TIPM module on this car? Here is the fuel pump wiring diagrams so you can see how the system works. Check out the images (below). Let us know if you need anything else.

What kind of problem are you trying to solve? If you have a crank / no-start, have you checked for spark?

The fuel pump relay is part of a safety system that shuts the pump down if a fuel line gets ruptured in a crash. The Engine Computer turns that relay on at two times. The first is for one second when the ignition switch is turned to "run". You may be able to hear the hum of the pump motor for that one second. If you do, you're done in that circuit. It's working. If you don't hear that hum, you can measure the voltage coming from the automatic shutdown, (ASD) relay instead. Look for the wire that is the same color at every injector, ignition coil, or even either smaller wire on the back of the alternator. That's usually a dark green / orange wire. A standard test light works best for this as most digital voltmeters don't respond fast enough. Back-probe that wire at any connector, then have a helper turn on the ignition switch. The test light should light up for one second, then turn off. What's important is it must turn on again during engine rotation, (cranking or running). If it does not, you won't have spark or fuel pump, or injector pulses.

If the test light does turn on steady during cranking, then it is possible to have just an ignition system problem or just a fuel pump problem. By far it is much more common for the test light to not turn back on. The typical cause is a failed crankshaft position sensor or camshaft position sensor. Start by reading the diagnostic fault codes. If you're lucky, there will be a code set related to one of those sensors, but if there is not, that doesn't mean both of them are okay. It can take a little time for a missing signal to be detected. When there is no code but a failed sensor is suspect, a scanner is needed to view live sensor data to see if the signals are showing up during cranking.

Chrysler made reading the fault codes yourself very easy. Cycle the ignition switch from "off" to "run" three times within five seconds, without cranking the engine. Leave it in "run", then watch the code numbers appear in the odometer display. You can go here:

https://www.2carpros.com/trouble_codes/obd2/p0300

to see the definitions, or I can interpret them for you. Let me know what you find.