There are 4 pins on the switch where the plug goes. 2 are to the contacts for P & N and 2 are for R to complete the circuits (start & backup lights). You should see continuity across the right pairs if the switch is OK. Otherwise it could get to be a pain should there be a problem in the wiring somewhere.

My old switch had oil, dirt, etc. in it, which likely prevented the contact (P &N) from making. Now the mystery is that the backup lights don't work with the new switch!! They were fine before.