You guys are right, the one-circle/two-circle subject is rarely discussed and that's an excellent write-up on it fuzeman. My only comment on it is the use of Nose to Tail or Nose to Nose terminology. When I hear nose-to-tail I always this of Nose to Tail Separation, not direction of turn. I think sticking with just one or two circle fight is a little less confusing, although many people do have a problem recognizing what's actually happening in flight.
I think the key to your choice of direction of turn is related to a couple of factors, relative corner velocities being the most important. Say you're in a fast plane with a corner velocity of 280mph vs an adversary with a corner at 220mph. The slower plane will out radius you quickly in a one-circle fight and staying near your 280mph corner velocity will do nothing but cause you to arc in front of him giving him the lead-turn option at each pass as he consistently works inside of you. By going two-circle you can maximize your turn rate by staying fast and gain greater separation then in a one-circle fight which gives you the opportunity for a slight high yo-yo when you're across the circle from your opponent followed by a slight low yo-yo as you come back. This combination will let you use the vertical to minimize your radius while maintaining e. My gameplan would be to make one or two merges staying at corner and watch my opponent. If he starts making significant angles at each merge that tells me he's selling his e. Once he's done that and has bled some then on my next circle I'll still do a high yo-yo but follow that with a little bit deeper low yo-yo. This gives me a little more e but sets my opponent up for a nose low merge while I'm comeing up nose high. Since I have the e and he doesn't this is where I'd zoom pure vertical and turn the fight into a vertical one with good e differential.
Also, another significant consideration when choosing between a one or two-circle fight is your roll rate. Say you're in a Typhoon against an airplane with better roll rates (that's just about any of the other fighters). Roll rate has a very significant effect on any reversal you need in order to force a two-circle fight. If your opponent rolls significantly better he can easily deny you the two-circle by simply reversing quickly. Also, the time you take to reverse (if you need to in order to force the two-circle) is time that you're not turning giving an additional advantage to your opponent. To maximize your ability to force a two-circle you want to avoid having to reverse and the best way to do this would be to go for lateral separation before the initial merge. This will virtually guarantee a two-circle fight, at least until the second merge. If you must reverse, do it as quickly as possible. Unload, slap in full lateral stick and use rudder to get the quickest reversal most planes.
Last, the two-circle fight also favors the aircraft with the best firepower. You'll have less merges (in the same period of time) but sufficient separation that makes it easier to get good forward quarter snapshots at each merge.