Only transfers are forbidden, other movements are not affected (eg. Govern the Unaligned at superior ). The vampire can become controlled if it reaches capacity, Brainwash stays on it (if Banishment is used, the effect resumes).
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Brainwash
Master.
Put this card on an uncontrolled minion in your prey's uncontrolled region. This card remains in play. No transfers can be used to move blood to or from that card. Any minion may burn this card as a +1 stealth Ⓓ action.
Rulings
You can only target a vampire by position, the target Methuselah can shuffle their crypt. If you have no clue (tokens, cards) about a previously revealed vampire's position, you have to take a bet. In case multiple copies of the same vampire are subject to different effects, the controller must track them, but they can do it secretly (eg. Banishment was used on one that would benefit from The Rack if controlled again).
A brainwashed advanced vampire can still merge with their base version in play.