To check your current switch, mark the three terminals (how doesn't really matter) so you can ID them going forward.
Then use your multimeter to see which terminals are connected in what key positions.
Example:
Key out: no terminals connected
Key in, position one:
-terminal 1 connected to terminal 2
-terminal 3 unconnected
Key in, position two:
-all three terminals connected
If you can give us that info, we can help you further.