First thing, move the stick slowly through the gears, and see if at any point the lights DO come on...
Second, there's a contact in the reverse linkage. See if you got 12V coming in. If so, jump the switch, and watch the lights light up. If not, the short is between the contact and the wiring split-off to the 2 lights.
If not, use the old analog fallback electricity detector:
Never got a nickel for wrenchin', so I know nuthin'
Mine might be ugly, but it's slower than yours.