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Dragon is right, probably dont want to run that kind of load thru the reverse indicator.
So....sounds like the best way would be to wire another relay into the circuit, OR just have the light on a completely separate circuit that is independent of the reverse lights that you can manually turn on and off with the switch.
And in your drawing the wire running from the factory light needs to go to the aftermarket light, and then the switch needs to get power from the battery, the way you have it wired it will only come on with the reverse lights AND the switch toggled, you want the aftermarket light to come on with the reverse lights on or off right?
If this is a driving light you have to remember it is going to not be a very wide beam. As far as voltage is concerned there might not be enough to handle it to full power try the relay and see if that hepls.