I don't like to use the word failure , so I won't . Since you did not yet achieve your goal of getting your jeep running , I will state you did not as of yet complete your task . So far , you jumped a power wire to get the fuel pump to run to find out if the fuel,pump is working. It's working , so that part is eliminated . No need to change a fuel pump . You will have to go back to the power distribution center and verify that current is ACTUALLY flowing from fuse , to relay to fuel pump harness . Obviously , current is not making to fuel pump harness at tank or engine would start .
Use a computer safe test light ( so you don't spike any wiring to computer) and immediately as key is turned to RUN position , check that current is going across fuse . I'm working from a diagram from a '92 wrangler since I don't have a '95 , but it will be similar if not the same.
If current is making it across fuse , now check terminal 85 in fuel pump relay . Check the same way , key in RUN and immediately check for current . Incidentally , keep in mind the AUTO SHUTDOWN RELAY is tied in with the fuel pump relay , so it may have to be checked as well . Check terminal 30 in fuel pump relay this way to. Check all fuses as well since this '92 diagram is showing an ign. Lps fuse to supply power to the fuel pump relay. Your goal is to find where is power and where it isn't . We will not readily blame the power train control module , or PCM (computer) , you would only do that if all checks are complete and wiring and components found to be in working order. If you can get a copy of the wiring diagram for this circuit for this jeep from AUTOZONE, it would help you immensely . This is where current is delivered from and ends up at fuel pump. I would tell you to just jump terminal 30 to terminal 87 , but you must find current first . Since some of these wires feed back to the PCM , you must use care , and a computer safe test light. They are not expensive and should be at your parts store. If you do find power at terminal 30 , you may try to jump it , but again , a fused jumper is to be used . You are better to invest in a TEST relay , as they are safe to check in these procedures. To cut to chase ( I know you want to get this done ) , see if a buddy has a couple of known good relays lying around , to avoid having having to buy some until you know for sure if one or both are bad.
Replace one relay in fuel pump relay socket and the other in the auto shutdown relay. Replace ANY bad fuses with one of the correct value as well . Turn on key and listen for fuel pump . Hopefully you got it . Try to crank . Hopefully it will start . A fuel pressure gauge is helpful to have at this Point . Your not just looking for current . You want fuel to, but , no current , no fuel.
please try these checks and let us know what you find. If there is anything you may not understand for any reason , post back for our help. Best of luck , greg92jeepxj