Seems like ~every 10th time I start the car the 4x4 light is blinking.
Can't find a way to turn it off.
pushing the button w/the same 4x4 picture does nothing
No change in the way it drives...

 

How often do you engage 4wh drive? You should be doing it every month or so and driving for a mile.
It could be the actuator getting stuck, especially if you have difficulties shifting into 4wd.

 

Could be your battery is starting to go and has lost enough reserve capacity, so when you start the car there is not enough "juice" to test the solenoid for the transfer case. Happened to me with my GX470, and new battery solved the problem. Have the battery checked to make sure it is within specs and has reserve capacity.

 

It’s the actuator for the system to shift from 4H to 4L. Increasing usage doesn’t do anything to prevent this. In Houston, where is very hot and humid, it’s happens in the morning, but when I drive the car for a bit and then turn it off/turn it back on, it’s fine. The transmission and that part have heated up and the moisture is gone. There are some videos on YouTube of people taking it apart and fixing the metal contacts and applying more dialectic grease. It seems that the POST is failing with moisture as these age and the grease wears off. In one of the videos, it seems like there was arcing across the metal strip and the contact point.

 

Thanks... I'm in the FL Panhandle & I think this may have been a Texas car...
Is it hard to get to the actuator ?