Fuel pump does not stop and start, runs at continuous RPM (or nearly so, based on assumed ~14.4V charging voltage from alternator or 12.6V-ish till engine is running).
Your '98 should have a return fuel system where fuel line goes from the in-tank fuel pump sending unit, to fuel rail on engine, and there is a pressure regulator on rail, which past the mechanical (no electronic sensing or switch) set point pressure of 35PSI or so (is it 41PSI max? I keep forgetting), regulates that by letting excess pressure bleed off by fuel going out the regulator through the 2nd, return fuel line back into the tank. This is assuming a US model '98 SOHC... I don't know about other regions nor where Penguin is, since it changed from a return fuel line setup to in-tank pressure regulator with no 2nd return line (only a dampener on fuel rail) on US '99 model year.
The '97-98 fuel pressure regulators in particular, have been out of production for years and are very hard to find, most people end up cobbling together components from other vehicle parts because Ford's had a line permanently attached while others a removable hose, then hose needs a compatible fuel line connector added if not present. However I don't think it's fuel pressure, yet that is something easy enough to check, with a loaner pressure gauge from an auto parts store if you don't have one. IMO, low fuel pressure is more likely the pump or fuel filter rather than the pressure regulator itself.
I suspect you have a cylinder compression (sticking ring or bad bore??) or more likely injector problem, but would hook up a scan tool that shows realtime data to see if it has a code thrown or indicates which cylinders misfire. If it is two of them, on the same ignition coil (it's a waste spark setup) then I'd look into ignition plugs/wires/coil again.
Injectors, unplug the injector during a misfire event and see if it runs the same or worse. If worse, plug back in and move on to the next cylinder. Except, that's easier to do to find which cylinder, when there is a complete firing failure while you have intermittent problems instead, but it's still worth checking if it gets to this point. Compression, test it or a leak down test. If it's compression, I can only wonder about some problem during the rebuild.
What more is "serviced" the injectors? You only applied power and saw them move? Easiest first thing to try is probably dumping some techron fuel system cleaner in a half tank of gas (double strength) but if it keeps misfiring it could damage the cat on that bank. Might want to run it a moment, shut off engine, wait a few minutes, repeat that a few times, to let the fuel system cleaner sit in injectors while minimum unburnt fuel goes out a hot exhaust, or leave it running as long as it isn't misfiring.
There's also a fuel injector cleaning service that some shops offer. I assume you used new o-rings when you put the fuel rail back on? All else fails, it might need injector(s) removed and ultrasonically cleaned or replaced.
Are there any other relevant modifications to this vehicle besides rebuilt engine? If not, seems like your topic would have possibly gotten more views in the main 2nd gen forum rather than the modified subsection of it.
