'06 PR TRD Reverse whine

This is a recent development. If my truck has been sitting long enough for the engine to cool there is a low whine coming from the engine compartment when the truck is placed in reverse. It stops if it is in Neutral or put into Drive.

Toyota said they would have to keep it over night to test it when it's cold and I simply can't do that yet. Has anyone else experienced this so I can let them know what the deal is?

The truck is serviced regularly and well maintained. All fluid levels are normal.

Any help is appreciated.