Almost 24 years for a relay is a really good relay. That makes sense.
I realize all my relays are original...
When my fuel pump on my 97 started going out, you could hear it struggling; I'd turn the key off, and on, and off, and sometimes it would start fine.
I was really lucky it lasted long enough to get to the house the last time; It kept dying, but would restart after a few tries.
If you replaced it with a Cheap pump, it could still have problems.
Like Mikey said, the pump only runs for a few seconds; if you're not getting pressure until a few seconds after it's run, then you might have a crimped line or something.
Look at the fuel line near the filter location; one of my "buddies" helped me out with one by jacking the car up with the jack on the fuel line.
Maybe it's restricted.
I had to replace the line.
Red '96 Cougar XR-7 240k mi. '02 4R70W, PST DS : '03 PI engine, 04 maf, 24lb injectors, 2.5" exhaust, '02 4r70w + Jmod, DirtyD0g TC + cooler + 3/8" lines, 255 walbro fp. Alpine system.
Black '96 Cougar XR-7 (Lazarus) 210k mi PI Intake, '02 4R70W, Jmod, PST DS, GrogTune, Konis, Mark LCA+Poly, racecougar Custom Engine Chain, and JL and racecougar Bracing.
Black '97 Tbird Limited Edition, '02 4R70W, 255 walbro, PST DS, PBR Brakes&SS lines, Toicko Blues & Springs, GrogTune.
"War Is Peace. Freedom Is Slavery. Ignorance Is Strength." - George Orwell.
Truth Isn't Truth. - Rudy Giuliani, 2018 Award winner, “Most Outrageous Diversion” by MSNBC for this quote