That is odd. On my 1994, I can see fuel pressure build on my gauge during cranking with the key in START. The gauge goes to 0 until oil pressure builds after starting the engine.It never turns on in my truck during cranking not until I added the relay mod.
The 96+ that turns on during cranking to prime.
I also have an "idiot" light wired to show the LP is getting power. The light comes on during cranking, goes out after the key goes to ON after engine starting until oil pressure builds, then the light comes back on.
IIRC, 1996+ factory LP wiring powers the LP during the glow plug cycle, too.