Yes, correct, but you can work it either way, either find the logic for pump activation or do a quick bypass and see what happens. From what I see on the attached, initial ECU gives a 3 sec HP run for self test and maybe priming purposes. Then main relay, sub relay, left hand, starter, also energizes HP sub relay, middle) via left hand diode, and after starter disengagement, HP sub relay, middle, continues to be energized by right hand sub relay, ECU, injector and ignition relay. The starter relay, which also affects the HP relay is also conditioned by the neutral switch. But if you have starter available, forget the neutral.
I´m starting to suspect that you hay have an ECU issue or ECU wiring issue.
As service manual is saying High pressure fuel pump is controlled by CKP sensor and TDC sensors 1/2 I'm wondering whether ECU/ECM issue or one of these sensors failing might be more likely problem cause?