The idiomatic English phrase "keeping vigil" means staying watchfully alert or guarding over something, which fits the context of armed policemen watching prisoners closely.
"Taking vigil", "Looking vigil" and "Guarding vigil" simply aren't standard English collocations, English speakers don't pair those verbs with "vigil" in ordinary usage.
Only "keeping vigil" is both grammatically correct and idiomatically natural here, which makes "Keeping" the right choice.