Did the relay fix it? Usually, you can just swap relays and see if that works. If it doesn't then you may have a fuel pressure regulator problem OR you may need to replace your ECM. All those can keep your pump in prime - just not with key off - engine off. So, it probably is the relay. Just wanted to know if that was the fix.
93 GT vert-.030 block, GT40x heads, E-cam
94 Explorer XLT-GT40P, 4R70W
81 F100-4.9 300
87 Buick GN-.030 block, 208/208, TE60, alky