13, 15 and 21 will not prevent starting. 41 will prevent starting, so that has to be cleared at minimum. However, the two tip-over sensor codes WILL allow a restart on cycling the key switch even though the code is still stored in memory provided the bike is restored to the upright position and wiring repaired. So I suspect you may still have an issue with the switch or wiring.
You need to toggle the emergency kill switch on the right handlebar, not the key switch. The codes are stored in the ECU and could just be from powering up the ECU while you were in the process of rebuilding. If they return after clearing, then there is still a problem with those circuits.
To clarify: An Aussie 2003 or a North American 2003? According to the respective wiring diagrams I have, an Aussie 2001 LAS should have the same connector as a 2003 NA model: Grey, 3 pins. Red/white to ECU pin 8, Yellow/Green to ECU 26 and Black/Blue to ECU 33. Part No. 5JW-82576-00.
However, Yamaha made changes starting in the Aussie 2003/NA 2004 model year. The ECU connector pinout was different (at least on the NA version) and the LAS was changed to Part No. 5PS-82576-01. This was used throughout the Gen II and well into the Gen III models. The wire colours changed slightly: Blue to ECU pin 13, Yellow/Green to ECU pin 26 and Black/Blue to ECU pin 33. From the schematic the connector looks the same, but that's just an artist's rendering so it could be a different connector. From the order of the wires it appears that the only change was the R/W wire colour became Blue, but there's no internal wiring shown.
Both service manuals indicate the only way to test the switch is by monitoring the value using the on-board diagnostic. Upright, the voltage shown should be 0.4 to 1.4v. It varies as the bike tilts and the ECU trips at between 3.8 to 4.2v. So it sounds like a potentiometer. Probably supplied with 5v from the ECU on one of the wires (R/W would be my guess) with the other two being the return signal. If any wire is broken or shorted the ECU does not get an expected value and sets a code 41. If the wiring is OK but sensor tips sufficiently, one of the sensor wire voltages rises, the other drops and the ECU sets a code 30.
As noted, use 62. The smaller numbers in the trip meter space display values according to the associated sensor. This is were you will see the voltage from the LAS, for example. If you are looking at the throttle position sensor, the value will change as you twist the throttle. Etc.