I would argue the MT clinch is borderline irrelevant in MMA due to wrestling. MT is basically the exact opposite of what you want to do when wrestling.
So clinch = Greco Roman with knees, basically. Probly have better advice on the grappling forum.
If you already were excellent at MT clinch, that's one thing. But for MMA, I'd learn the MMA clinch. It's kind of like people asking how to learn karate so they can fight like Machida, when in reality he spent 40 years perfecting something not that useful for MMA.
Can't agree on this one - Overeem, Matt Brown and Demetrious Johnson have had very good success with it - keep in mind proper muay thai clinching looks more like greco with knees and elbows (when it comes to positioning) than most people probably realise.
Here notice how he pushes and controls with his forearms into Baugotinov's shoulders to move
He does it again here, bicep control on the right both lifting it out of the way so Henry can't gain control and then covering it to land his knee.
Keep in mind most of those gifs were mainly using the plum, which is poor for control in pure muay thai because of how easy it is to reverse.
Holding a single collar rather than a double means you can frame and keep your opponent off you and land elbows
Tricky muay thai sweeps too.
Keep in mind that if you learn muay thai clinching and do it a lot with your MMA training it will only put you ahead of the curve, it's not so much that it's hard to learn so much as it is that a lot of western gyms just don't bother teaching it properly - but you can learn a lot if you're practising it regularly and looking at tips online, even if you're gym doesn't teach the subtleties too well.
But out of those three fighters, only Overeem came into MMA already knowing Thai clinching - the rest of them learned it - and I think it's pretty accessible, most MMA gyms are the bog standard MT/Wrestling/BJJ combination anyhow.
