... something or somebody. Is there a difference in meaning?
pine - definition of pine by the Free Online Dictionary, Thesaurus and Encyclopedia.
pine for something or someone
pining for a mythical past
She was pining for her lost husband.
COCA has 103 sentences containing 'pine for', and only one with 'pine over'.
I looked up the COCA (what a marvelous resource) and got one result containing 'pine after', too.