The important things in agitation are uniformity and randomness.
Remember, Uniformity and Randomness.
So, if you just keep doing the same repetitive motion, you are moving the same chemicals past the same film, and different parts of the tank get different amounts of flow. At 12 or 13 minutes, this may be less a problem, but at times getting down toward five minutes, it certainly can be. Anyway, you might as well develop good habits right from the get go.
Eventually, you wil absorb it into your sense of your body. No avoiding it. A long time ago (back in the olden days, when knights rode around upon their trusty steeds, jousting with each other and rescuing fair damsels from fire breathing dragons), I was sitting in a taxicab between Imogen Cunningham and Ruth Bernhard. There was well over 100 years of experience in that cab, and my part was almost 10. Ruth said "A young man asked me how I agitate my film; I couldn't think of what to tell him." Imogen said "That's interesting. I guess it would depend on whether the phone rings". I could picture her agitating film while watering her plants. I hope not cooking, because I sometimes had dinner with her. The point is that once you get it down, you will forget how you do it. When I resumed teaching after not doing it for awhile, I had to analyze how I did it. I'll share with you what I tell my students. They rarely have problems, but I think most beginners do have problems. I did; the memory is painful.
I use steel tanks which are perfect for inversion - they were designed for it. The agitation is accomplished by bubbles of air trapped in the tank gurgling through the reels. It will also work with plastic tanks, such as Paterson and Jobo, but I don't like Paterson tanks for 120 film. They are alright for 35mm. When inverting, I don't toss the tank in an arc, but rather exchange hands in the inversion, keeping the tank in one place in front of my chest. Try this with something like a can of tomatoes. You will see that as you exchange from left to right, or right to left, the can will rotate about 1/3 turn, always in the same direction, so in a 5 second time, you will rotate the tank twice or so. Just how many turns isn't important, but it is important that the tank turns. Imagine, if you had only one molecule of developer in the tank, how would you get it to contact all the film? That's a really good way.
I agitate for the first twenty seconds, then 5 every minute thereafter. Twice a minute is too much, I've found. Then rap the tank on the counter or the sink (not too hard! Especially if it, or the sink, is plastic). This dislodges any air bubbles that might stick to the surface causing hideous dark spots surrounded with lighter rings. These like to happen on the ends of your subject's nose, but never occur in gravel beds.
Oh yes. There are lots of creative agitation schemes, and they may be great, but I would very strongly recommend that you get the basic down first before getting into the arcane.
Good luck, have fun.
Larry
