^ That what I would try, would also check voltage first at pump when cranking & briefly starts as if no voltage or very low then that would indicate feed to pump when engine running has issue.
initial prime is time output from ecu & engine would run some seconds on the line pressure .
It started when you bought it as remember you saying about the knocking so not been stood long since then has it !
Everything points to wiring still not A1 (sparkies comment on battery issue bit off so his wiring may not of been perfect either) and if is wiring it probably easiest & cheapest fix .
initial prime is time output from ecu & engine would run some seconds on the line pressure .
It started when you bought it as remember you saying about the knocking so not been stood long since then has it !
Everything points to wiring still not A1 (sparkies comment on battery issue bit off so his wiring may not of been perfect either) and if is wiring it probably easiest & cheapest fix .