You tried to measure resistance across the battery terminals? Your problem is battery drain, is that correct? How did you determine the trouble to be in the trim area? Are you having any other symptoms? Do you know how to measure amperage? If you have a multimeter capable of measuring several amps you could introduce the meter between the disconnected negative terminal on the battery and the negative lead and check for draw on your battery. Depending on what boat/configuration you have, you could then begin removing components to see what component is causing your drain. Maybe you did this, I can't tell from your post.