i had some funnies when I wired the greens to the ign switch wrong. Would turn over but not fire. Would only fire when turned to ignition and started using a screw drive on the starter.
Wire colours on mine might be different to yours butshould be able to work the out with the lables on the back oy your switch to compare.
Sounds a bit unusual why at the off position, there's switched 12V just when you turn the key to ign but not when you first connect the battery.
I had a funny with the instruments whee the ABS light would not go off (Had to take the bulb out in the end to solve it). Try turning on the ignition without the dials connected and see if the switched 12V disappears.
The fuel pump relay is the only one out of the four that is switched.
This is how mine is wired.
Next step would be to unplug the relay pack and check the voltages again.