Fuel pump constantly cycles?

I checked 4 of the six, 2 on each side and they all had spark. The pump will run if I bypass the relay and I can only assume it does when it’s running, however it hasn’t yet, lol. This repair has been going on a couple weeks now, started as shutting off while driving, fuel pump would not work when I got it home, put in new pump and it wasn’t getting signal to prime with key on, that’s when I learned how to bypass the relay. It ran perfectly for about 45 seconds then would bog down and shut off. I'm sorry for only getting you a part of the info to start, I had been working with another mechanic here (Steve W) and hadn’t heard back from him in a few days, I hope the guy is ok, he’s been a big help. Anyway, it seems I’m chasing a ghost or a ground problem because symptoms and codes lead me to changing TPS, crank sensor, ICM, plugs and wires and cap and rotor are new, fuel pump obviously and filter, positive side of my battery cables. After putting those in my fuel relay started getting signal however it’s getting to many lol. Pre battery cable I was able to get it to run for the 45 seconds like I was saying (about ten times in a row) but after cables I am not getting it to run, although my pump is priming, lol. It's gotten well past frustrating. I’ve checked and cleaned a handful of grounds, I even ran a couple cables in tandem on the negative side to see if I needed to change that side, but it hasn’t made a difference. The only two grounds I haven’t been able to get to and probably are important are on the topside but behind the back of the cylinder head, there is so little room, but I guess that’s where I start again tomorrow.
Thank you for your help and input.

Oh yea, I replaced the ignition wire harness today and first crank it almost sounded like it wanted to go but it did not.

Last two codes I had were 1361(ic system low voltage) and 0122(throttle position sensor) which has been there since day one after clearing and introducing new codes and clearing them, it must be a wire I haven’t found yet.

Lastly, I used this method to come to the conclusion there is some kind of almost short in the ignition system because removing fuse 9 almost makes the test light go out, it goes very dim.
https://youtu.be/9wLrTjeb9TY

A little progress today, didn’t realize there were two different grounds at the radiator support and the one I didn’t already clean was the core ground support or something like that, the third negative coming off the battery, cleaned it & the mounting surface, now my fuel pump keeps cycling through the priming process only sometimes. So, I’m happy for a little progress, I'm going to try running a second core ground in parallel to it, just to check and keep looking for and finding grounds. Thanks again for the help.

I will do that tomorrow, Thank you for all your efforts and willingness to help me solve this crazy issue.
I know I threw a bunch of info at y’all and I I can’t thank you enough for jumping in, without even seeing a vehicle and offer excellent advice for those of us that aren’t afraid to give it hell however absolutely need some direction lol. I’ve done the majority of work on my own vehicles and the amount I’ve done grew with experience. I don’t mind getting dirty and enjoy learning, but electricity is by far my weakest skill set.
So, after installing the new ignition switch wiring yesterday, the first crank gave an indication that it wanted to fire but fell short. Today, after finding and cleaning the ground wire I had missed previously that came off battery negative, first crank did backfire, not huge but definitely backfired, no further progress though on the next few attempts.
This vehicle died while driving when this problem started under no crazy conditions, early morning, 6 miles into a 10-mile ride, no rain or anything that I could imagine would contribute to it. It’s bizarre man, did I mention that when I first put the new pump in, I could get it to run for about 45 seconds before it would bog down to stall, while running I could press the gas pedal and it would rev accordingly, when it wanted to stall, the pedal was no help. I was able to get it to run only by bypassing the fuel pump relay as it wasn’t getting any priming signal. Since replacing the positive side of the battery cables, pump is receiving priming signal, however now it won’t fire up.
Thank you for your time and I seriously mean that.

I will do it Joe. Didn’t get a chance to do anything with it today, because the rain shut me down. I’ll look into those things and have some video as well. Thanks again

Man, it was storming last night, had an F1 tornado roll through about ten blocks from the house, crazy weather.
So I was able to do a little checking, after finding, cleaning and re-attaching the core support ground( I even ran an extra one in case it needed some extra love), the shorting or I guess you call it an open ground circuit, that was observed by pulling positive post off battery and connecting 12v test light to the post and other end to the terminal, the only fuse that had any change was #9, IGN/BATT, and it would get very dim but not go completely out. We went away after redoing the core support ground. The only DTC code at the time was TPS sensor, which has been there since this problem started, even though I’ve put two different new ones in. Gave it a crank and ut basically just cranked. I can smell fuel, pulled three plugs from passenger side (2-4-6) and they were wet with gas. Now it gets interesting, # 4 plug was didn’t show me any spark, #2&6 did then come to find out the plug in 4 was cracked, ok I’ll accept that I probably over tightened it. I have some videos I’ll send also. While getting the video I noticed the plug in the #6 spot is arching through the plug boot I guess to the block, got a little footage of that and that kind of freaked me out because I never saw it before and plugs, wires, cap and rotor are new. Looking it up I guess it could happen because it’s a little wet there from the little bit of gas, but I don’t know. DTC code p1335 was added to TPS sensor and p1335 says crank position sensor however the guy I was working with here before you said that meant low voltage to ignition system & has me do voltage test for crank, ICM and coil, I’ll send those results as well as I haven’t heard back from him in a while and that’s totally fine, I appreciate any and all help ! Then the storm came and shut me down again. So, to summarize, had fuel and spark (in 2 of the three cylinders checked anyway) but no ignition. I’m just getting going down here today (in Florida) and I’ll send the video and results from test done previously and anything else I can find to you shortly ok. Thanks B again man I can’t tell you how much I appreciate you input.

When I noticed the arching, I had a different set of plugs in than the new ones as they had all been pulled, this is the plug that had the arching, and I didn’t even notice it has a little bit of a crack in the ceramic.

Cylinder #2 after I pulled it and pouring the gas out

#4

#6

The plugs.

Spark test #2.

Spark test # 4, no spark, cracked plug

Spark test #6 you can see the spark go to the frame because it’s too close, sorry about that.