Update: Replaced the pump and sender assembly with a unit from the junk yard. Issue solved. I thought these pumps would have been all or nothing. Never expected to have flow and no pressure.
The pump I removed from my vehicle was genuine BMW and looked very new. Prior owner must have replaced it not that long ago (the vehicle has 138K miles). Is it worth just replacing the pump rather than the entire pump/sender unit? I was planning to replace the entire unit until I pulled out what looked like a nearly new BMW pump/sender. I am not going to rely on the junkyard unit for long, but it confirmed my issued and got the vehicle going.