How do troop rotations to places like Japan, South Korea, Germany, Qatar, Kuwait work?

It does depend on the MOS and where the positions are located (Installation). Soldiers are reigned by the needs of the Army at a particular installation. Not all Soldiers will spend a day overseas. It is possible. Deployments depend on the unit the Soldier is igned to (FORSCOM units will deploy) and the MOS required in theater. Very rarely it is who you know. Ultimately, the Soldiers branch manager will requisition for a Soldier to report to a new duty station and the report date. Yes, some Soldiers do back to back tours in Iraq by virtue of their MOS.