While Zorba's solution definitely works, assuming your Auxbeam output handles enough current to drive the auxiliary reverse lights, you don't need a relay - the Auxbeam has a solid state relay inside it already. All you have to do is wire your auxiliary lights to the reverse light wires at the taillights and to the Auxbeam output (both in parallel). That way, your auxiliary backup lights will illuminate with either the lead from the taillights or from your Auxbeam. Easy peasy:
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Unless I'm missing something...
The original question - AS I UNDERSTOOD IT - was "how to convert a SPST switch into a SPDT output". But Hell, I probably missed something.