Needless to say the APU start sequence is well on it's way inside 60secs, but ONLY after the APUC has seen the actuator internal limit sw signal.
Not sure I follow you, McHale. The APUC activates the starter motor (after a start signal from the pilot). There is no input to the APUC from the actuator internal limit switches. The 13 degree switch is external. This does feed the APUC.
I've compared diagrams for 4 different airlines (basically all the same).
I understand Spanner's comment. The EICAS will tell you in a timely manner that the door is not fully open (a half open door is probably not an immediate problem). If the door is not even at 13 degrees, the APU starter won't activate.