I don\'t have the electrical diagram for a 6th gen Corolla with me - but does it have a 8-pin connector behind the switch?
If it does - then it probably is very similar to the 7th gen and 8th gen electrical connections (8th gen are the ones that I posted here). For the 4 keyed switch positions (LOCK, ACC, ON, and START) and assuming that you are looking at the connections so that pins are be numbered (top row) 4 - 3 - 2 - 1, (bottom row) 8 - 7 - 6 - 5
On position ACC, Continuity on pins 2 - 3
On position ON, Continuity on pins 2 - 3 - 4 and 6 - 7
On position START, Continuity on pins 1 - 2 - 4 and 6 - 7 - 8
But to be the safe side - pick up a copy of Haynes or Chiltons repair manual at an autoshop or at the library - should be a wiring diagnostic guide that you should be able to use. Given the age of the car and its behavior - probably pretty safe to assume that it is a bad switch. There is a small chance that it could be the wiring from the switch to main wiring harness. A quick visual inspection would catch most of that possibility - though buzzing the wires out with a multimeter would be a better method. Good Luck.