Does is strike anyone else as strange, sometimes, that these two should be friends?

I think it was clever of Emma Thompson to forge a connection between them of having served together in India to explain the bond and the friendship, but there's really no indication that there was every any link like that in the book.

Of Sir John, the narrator writes that as a sportsman "he esteems only those of his sex who are sportsmen likewise" so I suppose it is fair to assume that he and Brandon enjoy that together.

On the other hand, when we read that "Colonel Brandon seemed no more adapted by resemblance of manner to be his friend, than Lady Middleton was to be his wife", that seems obvious to me and I wonder at it too. He isn't the sort of lively young person Sir John likes to gather around for merry parties. Brandon is silent and grave where Sir John is full of boisterous mirth and likes noise and action, the more the better. Brandon listens attentively to Marianne's music, and Sir John talks all the way through her songs.