If you noticed in the beginning of the video I posted, he moved the shaft in a up/down movement, going with the cross… get the cross in a vortical position and push up and down, then rotate 90 degrees and do it again… that is why the wheels need to be off the ground…
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I never test for a bad U-joint using the twist method. It’s not conclusive.
I test by raising both rear tires off the ground, and then rotate one of tires back and forth to check for play and by spinning one of the tires very rapidly.
Tester
One mechanic said the driveshaft splines were worn. Could that cause the clunk?
I highly doubt the drive shaft splines are worn.
Have them lube the splines with lithium based grease to see if that eliminates the noise.
Tester
I push/pull on the u-joint under test in various directions as well as give it a twist, but I don’t orient it in any particular way first. Good advice, & easy enough to do, next time I have the rear wheels up, I’ll give your idea a try. I’m presuming removing the driveshaft from the truck and doing this test on the bench would work too. That’s on my truck’s-maintenance agenda.
Another idea, when I’m lubing the truck’s driveshaft, my driveway diyer method is lie underneath with truck on flat spot (no slope so it won’t roll) in neutral with no parking brake; then I push/pull on the truck chassis to slightly move it forward/backward & rotate the u-joint to an angle where I can access the lube fitting with a needle applicator. The angle probably has to be within +/- 5 degrees of perfect, otherwise the needle won’t reach the fitting. I presume that would be a good time to do the up/down push test too. Or is there a need for the wheels to be off the ground?
Why twisting might not detect a bad U-joint. I just replace the rear U-joint on my Silverado. The needle bearings on two opposite caps were completely gone, but the other two opposite caps were just fine. The two good caps, being opposite of each other made it difficult to detect any twisting motion.
There should be some twisting motion, but the gaps are so small that it is difficult to detect.
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The latest mechanic says it’s the rear drive shaft. $1400 to replace.
They’re jacking up the price on the part, (which is to be expected), but gouging on the labor.
Find another shop.
Tester
Good grief. Perhaps I’m out of touch but what goes bad on the driveshaft assembly? the U joints. There’s an expansion coupling on this one I think but that’s unlikely the reason for your clunk.
Instead of R&Ring the driveshaft assembly with new U joints at a fraction of the cost, just replace the entire assembly for $1400 
Parts swappers.
If replacing U joints is too difficult or out of skill set, find a place that fixes them. The last place I lived, there was a driveshaft repair place not far away. Drop off the shaft and they replaced all the U joints and balanced it for not a whole lot of money. Did a brisk business. They made a few custom driveshafts for me. Saw lots of people come and go, even the local shops went there from time to time.
Taken to the extreme- my truck clunks going from reverse to drive- you need a new truck 
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So here is your answer(s). It’s the u joint, it’s the drive shaft, it’s the rear end. It’s normal. It’s not normal. So take your pick.
Of course most are not fans of just replacing parts in the place of a diagnosis, but … I suppose u joints are more now than 20 years ago, but what I would do is just replace them. If ya gotta get a new drive start after that, not much lost since you’d replace the joints with the shaft anyway. And if that doesn’t do it, it’s the rear end and normal.
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What’s wrong with it? About the only thing that can go wrong is that it’s bent. That’s unlikely. If they didn’t tell you, ask them, saying that you are thinking about it and want to undergo the issue better.
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Napa’s highest price rear driveshaft is
NAPA Solutions
Comments: Rear
Per Car Qty: 1 NOE 70077221
List: Unit: 869.99
I’m sure that any hop will mark it up some…
The labor to replace it is only 1.1 hours…
So I could see it getting to $1400…
But I would look for a driveshaft shop that builds racing/custom driveshafts and see what they charge… Or a pro shop that still replaces u-joints… lol
I agree.
The video that john_184618 posted a few weeks ago has visible play between the joints. I would focus on a good mechanic who can inspect that joint.
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If a pro mechanic who has actually inspected the vehicle on their lift says replacing the driveshaft for $1400 is the best option, my guess, that’s probably the best option. IMO OP would have to have some solid evidence based on a second opinion (another mechanic also doing a shop inspection) to do otherwise. For example the inspection could have shown all the driveshaft’s u-joints, the expansion joint, and possibly a splined connection to the transmission or xfer case, all have some play. Not a single-part problem in other words.
It’s possible the clunk will remain after spending the $1400 of course. But at least OP will have a new driveshaft, making it easier to diagnose what’s really causing the annoying sound.
If OP was given an inspection report, could post that info here of course for more ideas.
Again, no more opinions. Just replace the u joints. Even the best ones are only. $20-40. You can do it yourself and save money. All you need is the proper sized sockets and a wide vice or press. Just do it. A couple hours. Yeah I don’t like laying under a car either but it’s either that or pay someone.
And once the driveshaft (propeller shaft) is off the vehicle, each u-joint pays 0.5 hours, so 2.1 hours total to replace both u-joints… At $200 an hour and overpriced u-joints, should still only be around $600 + tax…
fyi, Googling ‘07 Sequoia driveshaft’ shows links to some lower-price replacement drive-shaft options.
Thanks everyone for your input. It is much appreciated. I’m going to speak to the mechanic tomorrow to get more information. It is a licensed establishment that’s been in business for at least 30 years and has a good reputation. However, I need to understand more about what’s going to be done. A google search shows estimates ranging from $200 for diy up to $1500 at a shop. I live in a vacation area where everything is expensive.
Just like my neighbor, you may run out of people that will speak to you over a simple u joint replacement. There is not a whole lot to explain. Out with the old, in with the new. Don’t ever mention replacing the drive shaft though. Over and out for me.