Just to add on to what Hellraiser and Daryk have already said: your logistical staff handle what you seek. In US military terms, that is indeed the S-4 for battalions/squadrons and brigades/regiments. For companies/troops, that will be a combination of your supply section along with the XO and senior enlisted advisors (e.g. first sergeants) and at the platoon level, your platoon sergeants under the tutelage of the aforementioned company supply sergeant/section. If a squad ever operated on its own, the senior team leader would likely be tapped for the job (but that isn't something that happens at the level under question).
Military police are not pickets. They control EPWs (prisoners), secure routes (like state/highway patrol in law enforcement, but with a focus on security and integrity of the route and the vital military traffic, not traffic law enforcement), and act as police in a military context, especially in garrison. Pickets--not really a US military term in common usage--can be any element that is providing some aspect of security forward of a given force's main line of defense.
(In Team Yankee, that was indeed a divisional cavalry squadron; in real life in the Fulda Gap, say, that would have been the 11th ACR.)
Since I am more familiar with how an armored cavalry squadron/regiment does things at such a level, I'll use that as an example (but if you want to know how an infantry company does things, you can extrapolate easily from this).
Everything a US military unit does (any service, at any given time, but especially the US Army combat arms) is controlled by the Operations Order. That includes where things like the logistical units will go, where the TOC will be located, who will do the site reconnaissance before investing a location, where units will be positioned for defense, how much supplies they will get and how and when and where they will get them. Things like latrines and exact positioning of tents will be according to SOPs and local lower-level leadership initiative. I think this is the real answer to your question. Boilerman does not have to tell you, either: your higher headquarters will tell you everything you need to know. It's just that sometimes you will have to drag it out of them. ;D
The commander (of the squadron or regiment as desired) will choose a general location for the command post (CP, but usually called the TOC for Tactical Operations Center) which will effectively define the unit's "rear area". The operations staff (S-3) will be responsible for setting up the actual TOC site, while the S-4 sets up the logistical element (which will become the "______" Security Area). The S-1, -2, -5-. and -6 kinda hang out and follow the Three Shop around until they stop moving ( ;) ). The S-3 and -4's senior NCOs will be setting up things like the chow hall, and the Unit Sanitation personnel (accorded those honors through an arcane decision-making process that is opaque to all who finds its gaze cast upon them) are responsible for setting up latrines or slit-trenches at every level (down to platoon, if the platoons are operating in their own patrol bases).
Unit or Element commanders/leaders choose areas to be protected and the noncommissioned leaders are actually in charge of digging fighting positions ("foxholes"), which are then checked (sometimes, often enough as time allows) by the commissioned officers.
Again, as stated (by Hellraiser), each level gets its data and goods from the next level up: Brigades supply battalions which supply companies, which supply platoons, and platoons supply their squads. That goes for orders, positions, and supply (of all classes, I-X)
If you are a merc unit of one, you still have to do everything that needs to be done for a regiment, you just have a fraction of the requirements. You need to know where your supplies and coming from, and how and when to get them. You need to know how you will get to where you need to be, and what to do when you get there. You need to know the chain of command, and how they will interact with you. You need to know how and where to take care of personal hygiene. It's just that you have to do that yourself. The good news is many adults can do all that, you just have to consider that someone may be trying to kill you at various points along the way.
A mercenary unit of any given size will simply have to get the job done with the personnel on hand, be them the equivalent of a lance, or a company, or a short division. The smaller the unit, the more hats its personnel will wear, just like a normal civilian company. All the facets of running a business or a brigade apply to a company (be that three people in an office, or a hundred sleepy-eyed killers in the woods).
If you need something fast for your Jump TOC (mobile headquarters vehicle), can't you just use a Karnov? It's got seven tonnes of capacity of the assembly line...? But a Heavy Hover APC would draw less attention and be functionally as fast (which is ridiculous, but, well, BattleTech).
