Ok Jack, as the “splice” is a DIY modification then who knows without the information on the colour of the wires involved, why perhaps the previous owner will tell you.
So from the fuel pump relay there’s a pair of white/orange wires in parallel, one to each o2 sensor, from each sensor you will also find a blue wire going to their respective terminal at the efi ecu., you may not see the colour as this wire is screened, there’s a third wire at each sensor with is earth.
So if u have a dodgy connection at the relay just repair it buy remaking the connection + replacing the relay if necessary, simple.
The fuel pumps earth connection is via the inertia switch, so why there’s a spliced connection there who knows, so what colour wires is the splice terminated from and to ?
White/purple is incoming from the pump at the inertia switch, the other wire is black so to earth... if the switch is activated the fuel pump stops.