Strange, we don't really try too hard to go for the full two-hands-behind head when we clinch at our school(Fairtex affiliate), if our partner leaves it open of course we'll take advantage of it but we usually focus on controlling the shoulders/arms/head to land knees or execute spins trips/sweeps and dumps.
Outside of MMA i hardly ever see anyone get a full-clinch put on them if both guys are good clinch grapplers. Look at the high level Thai fights for example, no one ever gets anyone in a full clinch, it's too easy to defend against & counter, it's always the 50/50 clinch or working on controlling the arms or spinning/tripping the opponent.
Note: These tips are mostly for straight-up Muay Thai, MMA has a wrestling/judo element so your experience may differ if you try this in MMA.
-Best time to spin your opponent is when he's throwing a knee, or right after you've engaged the clinch or pummeled in. Spin to the OUTSIDE, ie the side he isn't kneeing with. Remember, don't PULL him, TURN him, think of a car steering wheel. Make sure your hips are close before you spin him or you'll waste too much energy and struggle trying to spin him because you'll only be using your arms, it should be EASY to spin your opponent.
-If your opponent leaves one leg too far forward, use an outside trip or footsweep, he'll fall for sure.
-Stay tall, loose and on your toes in the thai clinch, square your hips, keep your feet square too. When you go into the clinch it's a completely different game, you're NOT in your regular one-leg-forward fighting stance anymore, that's an easy way to get swept and dumped.
-Don't leave your chin up in the air when clinching (it's a good habit to keep if you ever decide to fight with elbows in the future), keep the head down but stay tall and keep the neck and shoulders strong.
-Use your shoulders to shrug your opponent off when he tries to latch onto your neck/head, don't just let him get grips on you. Push his fucking face away with the palm of your hand and violently rip your shoulder away if you have to, don't do this too much in practice though, be friendly with your partner.
-Keep your elbows in tight, you want to stay on the inside, work on cupping your palms and using them as hooks instead of grabbing onto limbs,
-Always practice your clinch sparring without gloves to develop the muscles in your wrists and hands for when you actually have to wear gloves. Getting used to the "touch" is very important.
-DO NOT interlock your fingers at any point, this goes double for muay Thai fighters, if it wont work while wearing boxing gloves, don't get into the habit of doing it. The grip should either be palm over palm or grabbing your own wrists.
-Another tip specifically for Muay Thai guys: Don't grab your opponents limbs with your fingers, this isn't Jiu jitsu, you can't do that when you're wearing boxing gloves.
-Don't allow space for your opponent to throw straight knees, if your opponent is blasting you with straight knees you are doing something horribly, horribly wrong. Aside from the engaging & disengaging from the clinch he should only have enough space to throw round knees an angled knees. Only create space if YOU'RE gonna knee. You're the one in control, it's all about control.
-For Muay Thai guys: When you clinch spar DONT hit your opponent with the tip of the kneecaps, use the meaty parts of your thighs and the sides of your kneecaps, this is proper clinch etiquette in thailand. There is no need to injure your training partner, he is the most valuable piece of equipment you'll ever use.
-If your opponent ducks under your arm gets you to where your arm is trapped across your face/jaw (like a standing arm triangle), DONT TRY TO KNEE BACK, FOCUS ON ESCAPING, DRIVE HIM FORWARD, GET THAT ARM BACK.... that's a "you're fucked" position, you don't wanna be in that.
That's everything off the top of my head, but there is so much more to it, the Muay Thai clinch is like learning a completely seperate martial art. You can have the best boxing and kicks in the world, but if you can't handle when your opponent closes the distance and smothers you with the Thai clinch, you're in for a bad night.