Brake Light Fuse Blows When Backing Trailer

The first time I towed a trailer with my 2006 Tacoma, the brake light fuse blew when I shifted into reverse. I didn't know it at the time, but my gear shift was also locked in PARK because of the blown fuse. I have a Tow Ready T-Connector with a 4-pin flat connector. All of the lights, tail, brake, R & L turn, work absolutely fine as long as the vehicle is not put in reverse gear. What is it about Toyotas in particular, that this is an issue?
My reason for the above question, is that I have a son, living in Oregon, who is the owner of a 2013 Tacoma. His vehicle came equipped with the towing package, and has the standard 7-pin plug. Using a 4-pin adaptor to tow his boat trailer, he experienced nearly exactly the symptoms as I did. He has used the same 4-pin adaptor on a non-Toyota vehicle to tow the same trailer without incident.
In both cases, the trailers are wired correctly and are properly grounded, and the wiring in both trucks is also good. I've checked for any voltage on the ground wire when my truck is in reverse, and there is absolutely none.
If you are aware of a common issue that might be causing the brake fuse to blow in both of the above vehicles while backing a trailer, please comment. Thanks!!!