There are several different tomme styles. Tomme de Savoie is an Alpine tomme (from the Alps). The other main tomme style that uses that name directly is the Pyranee tommes which are harder in general (and often made of sheep's milk). In Italy there is also a "toma" style, which is sometimes similar to a Pyranee tomme, but can sometimes almost be like a grana.
"Tomme" is the technical term for the slab of curds that you remove from the vat. A "tomme cheese" is any cheese which is essentially just the tomme that you drain with minimal pressure. Because the tomme is just a single slab of curds, you normally "pitch" the curds. This means that when you've almost hit your pH targets, you let the curds fall to the bottom of the vat and let it form into a slab under its own weight. So normally there is a period of time where it's just draining in the vat. Then you remove it from the vat, let it drain with just enough weight to close it. This is why tomme cheeses often have mechanical holes. Most tomme cheeses have a natural mold or brushed rind.
Because it's such a vast style, I haven't really been able to study it in a lot of detail -- only a few specific substyles. My impression is that most tomme styles have a very high pH target at draining (often in the 6.3-6.4 range). They have a fairly long drain time to get down to a pH of about 5.3 before salting (though I think some styles may go lower... maybe?) They are tricky to do well because very subtle changes can produce outsized differences in results. I personally think there is also a lot of overlap in technique with many of the other Alpine styles in the North, or grana styles in Italy, but the result is quite different.
I think generally the main things to consider are: 1) high pH at drain, 2) pitching the curds for a good period of time and letting it drain in the vat 3) minimal weight while draining/pressing 4) appropriate rind treatment.
Rind treatment on a tomme is an artform, IMHO. You want to do as little as possible while at the same time effectively steering it in the right direction. It takes a lot of practice/experience to do well. Purchasing rind preparation yeasts and/or something like PLA or Mycodore is completely reasonable if you've never done this stuff before. You can also build up the natural flora in your cave, but my experience is that it takes 2-3 cheeses in succession to really get it going (after that, you really can basically do nothing).
My experience has been that Bantams is right (of which there is no doubt ;-) ). 5 months seems to be the magic spot for a tomme. Before that and it doesn't develop that distinctive tomme character. Much beyond that and it also loses it. I've done *many* tommes to the 3 month mark when I was learning how to do natural rinds and the cheeses were always good, but lacked the tomme character. Once it gets to 5 months, though, it's pretty surprising how different it can be.
Aris, I think you will really enjoy doing this style.