I bought a new 2008 Tundra. We also have a 2008 Land Cruiser, but do not use it to tow.
Our Tundra's 7 pin plug also did not work. I went to the manual to locate the fuse. It was blown. I replaced the fuse and it worked perfectly, afterwards. When we sold the trailer, the new owner had a later model Tundra. The Brake Controller was plugged into the plug on the left side of the driver's side and worked perfectly.
I would recheck the fuse. It has been 8 years, so I cannot narrow down the number or where the fuse was or even which fuse box. It may have been under the hood on the Tundra.
I would expect the Tundra and the Land Cruiser of the same year using the same system.
The blown fuse did not affect anything else... but the Brake Controller.
Since no one has responded, this is the best I can do. Like you, the fuse. If not the fuse, maybe your Brake Controller, if new. Try someone's Tundra / Land Cruiser. I did not expect this when I hooked up our 23 foot Airstream to our new Tundra. I feel the frustration... Since there are few Land Cruisers... a Tundra problem may come up to help.