If you're not able to change stations or any other settings while its flashing, sounds like the deck has a short or something going out somewhere inside. Not much else that would cause this, there's really only 3 things that would cause it to flicker and not respond.
No ACC+12VDC
No constant +12VDC
No ground connection
These three are the only inputs to the head unit that could be fixed if it were the problem, but because the deck is working, its impossible for any of those to be the problem, which means deck is bad.
Two options for ya at this point, either take it to dealer when its doing this, or at least take a video with your cellphone to show them what's going on, show in the video which buttons aren't working.
The other option is to take your 4runner to the nearest car audio shop and have them slap something nice in there! A decent shop should have everything in stock for the 4runner and should be able to install a deck wired to stock speakers within an hour or two.
If you have the JBL with Entune, they may need to order some extra cables in, but still should have it within a couple of days. Depending on how expensive a head unit you bought, shouldn't be much over a hundred bucks for the wiring and speaker cables and dash kit, including installation of all that.
