Ian,
See if this helps.
This is also from the same Electrical Book as before but shows the neutral safety switch.
They may have used two different switches, one without the back up wire connectors but I would doubt it.
Note on the diagram the two wires I have marked. If you have 4 wires off of the neutral safety switch then the two black ones not connected are for the back up lights. The other Blue-Red wires are already connected (or should be if someone has not bypassed it altogether which would be dangerous as it would start in P,R,N or D)
There is not a separate back up light switch as with the Standard and OD. It is all done with the neutral safety switch.
Check the power there in the black wires as before with the ignition on, lights on ad in reverse. If there is no power then the neutral safety switch is bad or the contacts are not aligning with the shifter in the Reverse position.
As Paul stated there "should" be connectors in the 14405 tail light assembly harness already.
Also look at "G" call out in the 1st diagram I posted.
Mine is a 56 with the back up assembly above the tail light but the wiring is the same.
Jim
Norfolk, VA
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"MABLE"
1956 Thunderbird Green / Brown Interior (ZE-XG)
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"MEAN GREEN"
1956 Mainline (FG-BE)