The fuel pump runs continuously when the engine is running to maintain a constant pressure in the fuel rail
The fuel pressure regulator maintains and adjusts the fuel pressure depending on intake manifold pressure.
It would not be a good or safe thing to hard wire your pump to run continuously.
The purpose of the bank angle sensor is to shut off the fuel pump in case of a tip over or crash.
Here's a diagram of the bank angle sensor and fuel cut-off relays on an SP1.
When you set the engine stop switch to the Run position, the bank angle relay actuates.
The ECU is what actuates the fuel-cut off relay (with help from the bank angle relay).
If the bank angle relay is working and so is the fuel pump, it sounds like the either the fuel cut-out relay is bad, or a wiring problem may exist.
The headlight relay is the same 4-pole type. Try swapping the fuel cut-out relay with the headlight relay to test and see if the fuel pump switches on.
And yes, there is a way to check for FI codes on your bike, although it won't tell you a relay is bad.
There should be a green 2-pole connector in the rear section of your bike.
If you short the two poles and switch the key On, you should see the FI light flashing to indicate any stored codes.
A long (1.3 second) flash is a decimal 10 place, a short (.5 second) flash is a decimal 1 place.
The ECU shows all FI codes in order from smallest to largest.