Cooking meat directly above the flame of a gas stove

I believe the goal is to get the best sear possible on each side of the meat. Moving the meat around too much could cause it to cook completely without getting a good sear on the outside.

Clearly this doesn't apply when doing anything "rotisserie" style, as you're trying to do the exact opposite: slowly cook the interior of the meat without burning the outside to a crisp or unevenly.

Also, see this similar question: Grilling burgers: flip once, or keep flipping?

Here's a couple of hints:

1. Learn to judge doneness by feel. See this answer for a good guide to temp by feel.

2. Learn to judge grill temp by hand. Hold your hand palm down about 3-4 inches above the grill. If you can hold it there for a second or two, it's hot; 3-4 seconds is medium; 5-6 seconds is low.

3. Sear first. Start with a very hot grill. You want about two minutes per side. Do not move the steak while it is searing. Make sure you've given the grill grate at least 5 mins to heat up.

4. Use a two level fire. Once you've seared your steak, you want to finish cooking over a lower heat. Build a two level fire by putting the coals on one side of the grill rather than the whole thing. Then sear over the coals. Then move it to the other side to finish. If the grill isn't wide enough for a two level fire, you could try quenching the fire by cutting off air flow. That will cool it quickly.

5. Finish with the lid on. This helps cook by heating the air rather than just using direct heat.

6. Change your fuel. Stop using lighter fluid. Use a chimney instead. Hard lump charcoal is better than briquettes. It's easier to light, creates less left over, and burns hotter.

7. Rest your meat for a few minutes before eating. Be aware that it will continue to cook during this time, so you want to pull it off a little early.

8. Read up on cooking steak. There are a bunch of good questions on this site!