I've been doing some of the same research, being on a MTT team myself. So here's some answers.
I actually just got some answers in regards to the requirements. It seems a unit receives a requirement to fill a certain amount of MTT slots with Marines with the appropriate rank, MOS, and are not too close to EASing to deploy. That's it. I asked this same question because it's my belief that this job is not for everyone, and there needs to be some requirements beyond rank and MOS. Take me for instance. I fulfill the rank and MOS requirements and requested to be on a MTT, but this is my first deployment and I have limited experience in my job beyond MOS school. Someone with at least one deployment under their belt would probably have been better, enthusiasm and genius can only take me so far.
Battalion MTTs used to consist of 11 members, but was recently upped to 15. They aren't always put together in the ideal fashion (sometimes they'll have two Log O's, or whatever) but what they shoot for is this: 1 Team Leader (0302, Maj), 1 Maneuver Advisor (0302, Capt) 1 Fires and Effects Trainer (0802, Capt), 1 Intelligence Officer (02xx, Capt) 1 Logistics Officer, 1 Comm officer, a Motor T/Logistics Chief (SNCO), an Artillery Chief (SNCO, usually 0811), an Intelligence Chief (SNCO, 02xx), a Comm Chief (SNCO, 06xx), and four 03xx drivers/gunners ranging from Sgt-PFC. Or something along those lines. For example, my team has a Major 0302 Team leader, a Major Comm officer, a Major Logistics officer, an 0302 First Lieutenant Maneuver advisor, an 0802 First Lieutenant Fires and Effects advisor, a Second Lieutenant Intel officer, and so on.
We do have assigned S-1, S-2, etc. functions to handle the day to day running the team. Some of those will carry over to the Iraqi training. I'm the S-3 for training, while the Maneuver advisor is the S-3 for operations. His Iraqi counterpart will be the IA S-3. The Log O will obviously be paired with the IA S-4. As an 0802, I don't have a "natural" IA counterpart in an infantry battalion. It is up to my team leader what I will be doing. Some MTT teams have a set advisor for each IA Company Commander, some don't. It's up to the team and the situation.
MTT teams are usually augmented with a few more bodies. Who they are depends on the support Coalition unit. Some get Army FOs. Some get ANGLICO teams. Some get Marine grunts.
I hope that answers some questions. My team leaves for Iraq in late November, so feel free to ask more questions before then.
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