Not that it changes your argument, but note that that diagram is from a old version of the Installation Manual. And the green LED has been added by your OEM, it is not in the Rotax drawing.
Your aircraft POH is wrong: The Back-up switch must be off for starting and for the entire flight. it is for emergency and ground maintenance use only.
Is the confusion due to Rotax showing the master switch instead of a master relay/switch combination? Maybe this was done as some OEMs use a large mechanical switch instead of the standard constant duty relay? I don't know but the drawing is correct; the starter motor should be after the master (you should not be able to power the starter with the master off)
The back-up switch wiring is correct in the drawing you provided, I am not sure why you say pin 2 and 3 are swapped?.
The back-up switch is poorly named: it is not for a separate battery, it's function is too bypass the fusebox relays and provide battery power to the fuel pumps and ECU (for redundancy) and also provides a means of powering the fuel pumps and ECU for ground maintenance (such as fuel pressure tests and ECU downloading)
