How thick are the cuts of steak? 1"? 1.25"? 1.5"? Also are these rib steaks on the bone, or boneless ribeyes? That will largely determine how long to cook them for, which is the key thing, along with letting the steaks rest to evenly spread the juices. And, is this a gas grill or charcoal?
First of all: Ditto on the not marinating aged rib steaks. Oh no no no no.
Second: If possible, let the steaks come to room temperature or close to it before grilling them.
Me, I keep it very simple. If I had 2 to 3 rib steaks on the bone cut to 1.25" to 1.5" thickness and my backyard gas grill, I’d do this to achieve what I consider medium rare steaks:
0 - Turn on all burners on my grill and shut the lid to preheat it. About 8-10 minutes.
1 - Rub steaks with coarse ground black pepper, garlic (either finely chopped/minced or just garlic powder), and a dash of cayenne pepper and (this is my personal magic spice) curry powder. Then, just before they go on the grill (or even after they come off the grill), a few sprinkles of salt.
2 - Lightly brush the steaks with extra virgin olive oil. Or spritz, if you have one of those olive oil spray thingies. Usually i just drizzle a little bit on the one side of each steak, then use the unoiled side of the other steaks to rub the oil around on the oiled side. That way both sides are lightly oiled. Then I run the edges of the steaks through the little bit of extra oil that rolls off onto the plate during that rubbing.
3 - By now the grill should be hot. Turn the burners down to 3/4 and toss the steaks on while CLOSING the lid to maintain maximum heat.
4 - 3 minutes later, open the lid and flip again.
Now the rest depends on how thick the steaks are. If they’re boneless steaks and only 1" thick, that’s it, steaks are done grilling. For 1.25" thick steaks, I grill another 2 minutes a side with the lid open. For 1.5" or thicker steaks, I will turn off the center burner(s), put the steaks in the middle over the turned-off burner and leave just the two burners on the outside on at HIGH. Then I shut the lid and cook for another 3-4 minutes a side (indirect heat).
If the steaks are on the bone I upgrade the cooking time as if it were thicker, otherwise the meat next to the bone is much more rare. Also if I were making steaks right out of the fridge after getting home from work.
Remove steaks and cover with tinfoil for about 5 minutes. If the cuts are very thick or on the bone, let them rest a bit longer, but for steaks cut for single portions each I wouldn’t think you need to rest them longer than 10 minutes even for thick cuts on the bone. This isn’t a prime rib roast!