Mustang fuel pressure is supposed to by 40 PSI (delta or intake referenced). However, you are using an external fuel pressure gauge that is Atmospheric referenced. Remember that the intake is under a vacuum at idle.
Atmospheric-gauge - intake-vacuum = 40 PSI delta.
40 PSI Delta - intake-vacuum = Atmospheric-gauge.
In otherwords, it's completely normal for the gauge FP to be lower at idle. If you do not understand the difference between delta and atmospheric pressures, then this will continue to elude.
Try this for a TEST. Disconnect and plug the fuel pressure sensor vacuum reference line. What is the fuel pressure now? Does it jump to 40 PSI? Note, never drive the car with this reference line disconnected.
Now the fact that FP is zero after a cold soak indicates fuel pressure leak down. This is either leaky fuel injectors, bad FP regulator, bad FP check valve, or bad/weak fuel pump.
Also, it would be handy to know what the intake vacuum is. It seems to me that the fuel pressure should have gone up more when the throttle was blipped. We need to know if there is something wrong with the motor itself that is causing very low intake vacuum.
Consider running a compression test.