It’s a reference to trim on a boat. The basics of which is that when you throttle up a motorboat, the bow (nose of the boat) will tilt up. You can adjust the angle (trim) of the engine to bring the bow down (or up). There is some more nuance than that, but that’s enough to get the joke lol.

To drink down means to bring the bow down. Instead of yelling “trim the bow” he is yelling “trim the bowl!”