The towing converter box is in the rear cargo area, passenger side, behind side trim panel. The part is shown in the parts catalog but there seems to be a bug since it's not identified in the catalog. It's just the picture but no part number or description attached to it. If the converter box is like the earlier RX330/350 models, there were two different boxes. One for vehicles with the towing option (TO) or without. If a hitch was installed on the RX without the TO option, the brake lights on the trailer would not work. The converter box needed to changed in order for the brake lights to work.
Unfortunately, due to this catalog bug I can't tell if there is more than one box. I hope your RX came with the TO option.