Should the door fail to open within 60 seconds, or open to a position less than the minimum 15-degree position, the electrical circuitry of the APU control unit is such that the APU will not start and the EICAS fault message APU DOOR will be displayed.
After the air inlet door opens, the APU controller does the APU start sequence and supplies 28V dc power to the starter motor.
Again this comes back to the definition of OPEN and which switches are used to show open. The wiring schematics don't seem to align with Spanner's notes.
747-400 Wiring Schematic 49-15-01 shows door position switch S1598 sending a signal to the APUC (on pin D11). The switch has the note "Shown closed <13deg". So we can assume that OPEN is 13 deg or greater.
On Wiring Schematic 49-11-02, the APU start system is shown. Inside the APUC, the driver for the APU starter relay has a logic "AND" gate with one of the inputs labelled "APU INLET DR OPEN". I take from this that the start system is looking at the 13 deg switch "S1598".
Then we have the switches on the actuator (Wiring Schematic 49-14-01). Some control actuator power and some are used to generate the "APU DOOR" EICAS message. One switch is labelled 15deg, but I don't see it affecting APU Start (as mentioned in Spanner's notes). None of these switches feed into the start system.