From the description it seems the system is not holding pressure when shut off, that could be a bad check valve in the pump assembly.
A pressure test would show you that, Just connect the gauge to the port. Start the engine and let it run a minute or so. Shut it off and if the pressure drops real fast you have a bad check valve.
But that will not cause a P0191 code.
P0191 is set when the ECM sees a pressure lower than 20 psi or higher than 70 psi.
I believe the problem in this case is either the voltage or ground to the pump control module or the module itself.
Here is a nice video showing this system and some diagnostics. Much easier than typing it all out.
Monday, January 23rd, 2017 AT 9:43 AM