Update

Been driving the truck on our property for two months. Stopped using the key fob to see if that was the issue. Two days ago it shuts off again. This morning husband tries it and it starts right up.
Still have no clue what the issue is.
The mechanic had surgery on his shoulder so waiting to see when he can get to it. Going to check with another mechanic to see if he might know anything about it.

 

Not sure of the inital post background but I know the gen 2's came with a primary key, and a valet key. The valet key will not work continually. I was Stumped. But found out after a lot of aggravation. Maybe it's something like that.

 

Do you have a picture of the key you're using? Here's something that might be useful...

 

Here's another thread about the key...https://www.tundras.com/threads/tundra-key-types-h-g-regular.35759/