Typically the fuel pressure should stay steady. Or at least it does on Lycoming TIO-360s on airplanes. Get to ride on occasion in the pilot seat on one and I ask a gillion questions. But those pressure numbers never drop during warm up and rev ups for mag checks.
One thing I noticed is they turn on a booster pump prior to take off and landing that justs pressures from around 20 psi to 35-40 psi. But this is on a TIO engine.