If a sink is on a ship and the ship is sinking would the sink be a sinking sink?

Yes, if a sink is on a ship that is sinking, it would be considered a "sinking sink" in a playful sense. The term "sinking" applies to the ship as a whole, and since the sink is part of that structure, it would also be sinking as the ship descends. Thus, in this context, the phrase captures both the literal and humorous aspects of the situation.