On my TTSE, whenever it happens it is just an indication that it is time to service the tires with air and rotate.
I notice that it will go along and a few seconds later it will be gone. I believe (at least in my case) that it has something to do with turns on the highway and I believe it to be a slight imbalance that at certain times has the imbalance counteracting against itself and other times it is in sync with the opposite front tire.
Getting your wheels rebalanced has not seemed to be the answer for others for I believe that the slight out of balance situation is within the specified tolerance (or even the practical tolerance)[Ain't nothing in this world is perfect] but when the weight align you will get shimmy and after a slow turn in either direction it will go away.
Like I said, to make mine go away for a while, I find a tire rotation and air pressure check will do it for about three four thousand miles. And I do that at the first sign of shimmy. It has always worked.
A further assumption on my part is that the slight out of balance situation is aggravated by, or in conjunction with, uneven wear pattern on the AT's. Thus my theory and correction by rotation.
TRD alloy wheels and BFG AT tires as the vehicle was delivered. TTSE Stock, as delivered, no lift, no aftermarket parts.
If you let it go on and on without correction, parts are going to wear, get loose, and it will become more pronounced and readily returning.
I bought my 11 TT in Oct 2011 and very quickly developed a horrible steering wheel shake starting about 45 mph and not ending until about 65 mph Was under warranty and everything was tried conventional balance, Hunter 9700 balance, alignment, rotation, etc and nothing worked! Went to a suspension tire and servicing establishment that had been around for 40 years and dealer agreed to let me take it there.
Turns out, most tires coming out of the molds during about a 5 year period (supposedly not for last several years) that were/are "out of round" and previous named cures would not work. They knew how to "true" (shave) tires to get them within spec: but shop really needs to know what they are doing! Only exception at the time were Michelin tires and Goodrich KO's that came stock on my FJ had the problem.
Happy to report this cured my problem and haven't needed rebalancing yet 7 years later, Getting close to be getting some KO2;s before long
and they supposedly do not have this issue!
I bought my 2008 FJ 3 months ago - it came with some reasonably worn BFG KO2s on stock rims, and I experienced horrendous wheel shaking between 55-65mph. After reading about the flutter, or “Toyota twerk” on this forum, and how it was incurable (and recognized by Toyota as an issue) I pretty much gave up wondering if it was fixable.
Until I got new tires.
I now have Nitto Terra Grapplers (285) and all shaking has gone, at any speed. It’s like a different car now. So I’m not sure if this issue applies universally (or as much as I first thought) anymore. A well rounded, seated and balanced tire, with full wheel alignment as well could be the answer for many..