Most "vacancy" rules I've seen give the Board complete discretion to choose a successor to fill an empty seat...without regard for what % of the term remains.

That said, it's almost always a good idea politically to appoint the next highest vote-getter; the closer the event is to the last election, the stronger that recommendation. Though there's sometimes risk the appointee will join a minority faction, the legitimacy of the board is always enhanced by such a move, & a strong leadership will be able to capitalize on the good faith such a decision always builds.