If a player goes inactive and they were in a position of appointment, how long are they ineligible for the position? Is it permanent? Is it until 6 months?
They aren't ineligible. However, there are rules against appointing a placeholder whose sole purpose is to hold the position until they return.
Basically, when the position holder disappears, you are expected to appoint someone who intends to hold the position for the foreseeable future—not one who plans to step down when and if the original holder comes back.
As long as you do that, if the person appointed when the original position holder ends up stepping down for other reasons, there's no problem with appointing the original position holder again.
