If reverse is down and right, it's almost certainly a later tranny, so the switch is on the correct side. It may be faulty or may be misadjusted. Remove it and see if there are too many shim washers around the threaded mounting neck. If so, possibly all it needs is to remove a few. So test it while it is out and see if removing some shims, or maybe just threading it further in, makes it work as designed. The WSM details how to verify the adjustment and shim placement.
Tom
Tom