if you look at old daihatsu charade EFI wiring they have this second setup without the start relay, If I recall it only utilised a diode to prevent backwash or had a separate contact bridge in the igntion for STA position.
the wire to the fuel pump also ends on the FP pin in the diag box in the engine room, there are 2 reasons for it.
1 - test the fuel pump 12V
2 - prime the system for first startup after repair on fuel system.
If you notice after swap or working on fuel system on such cars they crank for about 30 seconds before the engine catches up. The correct procedure for this is to use a little wire bridge between 12V +ve or IG pin and the FP pin in the diag box, switch on the key for 10 seconds, switch off, remove the jumper, start engine - it will fire in the first crank.
Thats how I did it - usually people who did not knew said that the engine was so good it started on "half self" - lol...