It's true I've been scratching my head quite a lot about Greek aspect. Mostly I've spent my time with the aorist/imperfect distinction, but since you're asking, I'll tell you what I think about these perfects here as well...
First, the aorist imperative. φιμώθητι I think basically means "shut up!" (yes, it's passive, but let's no go to that). It's a single, punctual, delimited event, "STOP talking".
Then we have the present imperative, like σιώπα. There we have a durative action, "KEEP silent". "Don't talk and keep it that way!".
(I used the rude expression "shut up" because I think the common English expression "be quiet" is a bit ambiguous; I think that according to context, it could be closer either to the Greek aorist (shut up!) or with the present ("keep quiet!").)
The perfect basically represents a present state that results from a past action. πεφίμωσο would then mean "KEEP your mouth SHUT". It's close to the present in the sense that the action is durative (keep...), but there's the further nuance that it implies a past action that resulted in that durative state. Or this is how I see it.
Of course, when translating, you have to consider in each case whether you bring all these nuances into the target language, or whether that would be overtranslation...
Mk 4:39: καὶ εἶπεν τῇ θαλάσσῃ, σιώπα, πεφίμωσο...
"And he said to the sea, be quiet, keep your mouth shut!" (Do seas have mouths?)
Mk 1:25: Φιμώθητι καὶ ἔξελθε
"Shut up and get out!"