The boom operator (or boomer) can freely move around the aircraft. The boom operator position is usually accessible from the cargo hold and the operator can use the opening to move from his/her position. This is especially important for the KC-135 Stratotanker, which has the boom operator working in a prone position.
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While the operator is not fueling other aircraft, he/she has other responsibilities to carry out. According to the US military job description of a boom operator, the boomer,
Prepares and verifies load plans, directs cargo loading, and unloading operations, and inspects aircraft load to ensure hazardous cargo compliance and weight and balance status of aircraft. Ensures adequate safety equipment and passenger comfort items are on aboard aircraft. Instructs passengers in use of emergency equipment and emergency procedures.
among other things.
The boom operator is a specialist and his/her job cannot be done by anyone else on board. The operator also has to be qualified for the type of aircraft he/she is refueling. From interview of a USAF boom operator in foxtrotalpha:
Every receiver is a little different, so we have specific qualifications for heavy aircraft and fighter aircraft, called gulf and Charlie.