Krellik is tossing some awesome advice your way on the pummeling. The best wrestler I ever went against (in a judo class), actually pummeled with his head in addition to his hands and arms. It was almost like he was head butting me. He was one tough dude: collegiate wrestler, Iraq war vet, cop... he'd push with his head like a bull. Something to think about maybe.
Indead the head is an important part of pummeling and deffinitively a weapon that needs to be used in the clinch.
I just re read my advice and if you actually havent got that much instruction in the pummeling game I definitively could have been more specific and helpfull, hope you dont get annoyed that I elaborate a bit more even though you havent asked for it, when my head have started to spin I find it is always helpfull to write my thoughts down for my own sake to.
1. The basis for the pummeling is the simple "swimming drill", where you are starting out with one overhook/ one underhook, here it is the same as in the normal thaiclinch drill where you both swim hands, you both reach in for another underhook at the same time effectively meaning you both switch hands.
Even though the feel of digging your hands in is identicall as in the thaiclinch drill the posture is completely different, in the thaiclinch you want to be "dick to dick" with your hips thrusting forward into eachother, as upright and on your toes as possible and actively pulling back with your head.
In the greco clinch pummeling you are leaning into him, including with your head, and you are -driving- forward. You arent as hunched over as a freestyle wrestler looking to shoot, but you are indeed driving into him. Now if you are a big guy and used to not putting all your weight on smaller guys, stop that imediatelly and learn to put your weight on your partner as effectively as possible. If he is not doing the same you should be driving him into the wall. This dynamic is important for making the simple swimming drill dynamic, weight forward and driving.
2. Begin with just swimming with your hands, its complex as it is, no footwork, start out with ligth swimming, first thing you check for is if your elbows are flaring up to the sides (newbie warning) dont let them, pull them into your sides, it is like you are having a rubberband in your elbows pulling them into the sides. The difference in "light pummeling" and hard pummeling is that in light pummeling you are only having a light thin rubberband pulling them in, in hard pummeling you are squesing those arms into the side as hard as possible.
3. The object of the fast flow swimming is to get a fast flow into it, take some time and make sure you both get fluent in it, you can pretty soon go really fast, that is good.
-A finner point but that I found very helpfull in getting beginers to get more efficient in this is to look for a "double tap" in the swimming. What I mean by that is that in the pummeling motion since you are both going "from side to side" and leaning forward your shoulder is slamming into eachother pretty hard with each switch. That shoulder slam is your cue for taking your hand from the outside of his arm (your overhook) to the inside of the arm digging for the underhook. For me that means a simple small "steering wheel" motion where you make your hand thin and punch it straight through his armpit.
4. In the hard pummeling you are really making it hard to get the underhook this is a hard grinding game that builds strengthendurance. Lastly master a hybrid variation where you are making it rather hard to get in, but also are going pretty fast, this is a grueling variation.
Also somewhere along the way add footwork into it, stepping a small step while you are digging for the underhook.
5. From these variation start the "underhook wrestling" or simply the progression of pummeling where you are stop "swimming in unison" and instead simply are wrestling for position. Start out with simply having one goal, to clasp your hands together firmly in a double underhook. Both from the front, from the side and from the back (suplex position) with your hands clasped/bearhuged under his counts as doubles and winning the game.
-As soon as you start "wrestling live" this means you get more options for fucking with the other guys balance, this is good to do, since you both is driving into eachother the simplest thing to do is to simply step backwards or even better twisting backwards in one direction violently. Also play around with differnent slight changes is posture, where you are having your head, levelchanges, etc...
-Also you will notice that the swimming motion for the double underhooks is essential, but also let this "free pummeling" be free where and how you grip, play around with one underhook/one thaiclinch (collar tie) for instance, or grip one of his wrists or put your hands on his bicep and steer him that way like driving wheel, or any other thing you can think of.
This should be a loose playing but still intense and physical game, since you aint getting slammed, dare to play around a bit.
-You will pretty soon notice that going low with your head prevents getting in for the double underhook, so when you done quite a bit of just wrestling for double underhooks (several training sessions) add in more positional stuff, namely front headlock, and even the guiljotine later. (take the sub and get the tap), generally you want to add in more things to strive for slowly so the game remains focussed and simple. The most logicall are the tree mentioned plus snatching up a leg for the single leg (if you can snatch one leg you can also get the double but you dont have to slam the other dude).
-If you are on wrestling mats/tatami the logicall progression is to add in free sparring with throws and shoots where you start out clinched up.
-A great pummeling progression for basicly a complete uperbody warmup is light swimming/ hard swimming /fast-hard swimming (a few minutes of each, say 2-3 for instance) upping the intensity, perhaps then 5-10-15 minutes somewhere of free pummeling going fairly hard and then if you got the option free sparring with throws and shots.
...And I am not trying to sound like a wrestling badass in no way, but I helped start a small mma/submission wrestling club in a small town and plenty of months we only trained on concrete floors with a small padded corner for groundwork (that thin shit you sleep on when you camp and yogamaths, lol, but I learned a good deal on grappling while slipping around on that shit) and obviously you aint doing shots and throws on that. So to get as complete of mma training as possible we pummeled, and we pummeled a lot. Since a lot of people started and quit I got very good at breaking the pummel down and making it efficient.
And when we finally got out of the concrete "mine" as we called our first training ground we got to train with the local very good greco roman club that accepted us mma roughnecks. Altough none of us was really good in wrestling (mostly me that had held the pummeling part) and most of our guys only had trained months instead of the years the greco boys had trained, this focus on pummeling made our guys do suprisingly good in sparring with the greco boys. And not to mention the large chunk of the greco roman guys training was devoted to pummeling or "threading" that they called it in swedish greco lingo.
...Hope this helped. I found it helpfull to write it down.