If the captain of the ship is nowhere to be found (ie, not on the ship) and
you sink a ship as the first mate, shouldn't you get the reputation for
sinking the ship since you're in charge of the vessel?

Definitely not. What ever a ship does, its tied to the captain. You always
know who the captain is and to the captain, the ship is like his balls. And
the reputation is also really going to the ship, deferred to its captain as
its main pilot. How would we know the difference of who is at the helm anyway
to give the other officers reputation?

-- Lord Tarken Aurelius, the Sage

by whoever initiated the ram command? not really that difficult

Actually this is incorrect. The rep you get from sinking ships is personal,
and not tied to the ship at all (if what you are talking about is the +stat
"arr" rep and not the coins). This is simple and easy to show, in that if i
go and dock the ship i just used, and used some other ship, my rep is the same
level as it was before. Afaik, it makes the most sense for whoever is
captaining the ship when the opposing craft is sunk to get rep. Mates get, or
should get just as much experience at sinking ships as captains would....

Thats my 2 cents