Tested two ways. No fob and fob without battery.
Truck started both ways.
So, I obviously have an issue.
Weird how it sat overnight put battery in fob, doors unlock and it starts.
Now I am leary of it. Got a gremlin somewhere. My guess is going to be alternator.
I have a second gen Tundra as well, but I don't think that the FOB has anything to do with the immobilizer system as it's the key that's programmed to the receiver to enable starting.
That's a weird one for sure. Maybe your 12V battery is getting weak? I'd definitely do a load test on it.