4HI light just flashes on the dashboard -- any help?

Howdy --
Long time lurker, first time poster --

My family has a 2011 Sequoia SR5 4WD that's having a problem with the 4wd being "stuck", the 4HI light on the dash flashes continuously the whole time the truck is running. No matter what position the switch is in, it stays in 2wd mode and drives normally in 2wd. I pulled the fuse to stop the blinking, but it comes back immediately when the fuse is reinstalled.

--no other lights or errors, everything else works
--No clicking noises from the relays under the dash when you move the knob between positions.
--wiring, switch, and actuators all appear to be in good condition.
--no codes or CEL for anything.

I found an old thread on this exact problem but unfortunately it ends without a solution.

There is a brown relay under the passenger kick panel. I can't find any info on it, and if I search the relay's part number, the Olathe toyota parts website says it's not used in my vehicle. Is this the 4wd relay? Are the relays now contained within the 4wd module behind the glove box? I can't tell. Removing the relay changes nothing that I've noticed.

Please help! I'd rather not pay for a stealership diagnosis but I think I'm out of ideas. Thanks in advance.

Edit: I've already tried all the shadetree junk like flipping it back and forth a zillion times, driving it forward and backwards and such.

 

Check front diff fluid levels.

If the light is flashing that means that the cycle of operation to engage 4hi hasn't completed.

The transfer case has to engage 4hi mode 1st, then the ADD system in front diff engages.

Try this after checking fluid levels in front diff.

Chalk the wheels or get someone you really trust and a parking brake.

have them engage 4 hi. see if you can feel the transfer case to sense if it is engaging. a small thump or thud will be felt.

If you can feel transfer case engaging it is likely an issue with the front diff ADD actuator or shift sleeve.

 

reference material for how modern ADD systems work. This actually features Tundra system.

Four Wheel Drive Operation (4WD) - YouTube

Center Differential Transfer Cases - YouTube