Same sailor, or one of his buddies, used to live in my rig. I used two short pieces of of wood (8"X1/2"X1") and screwed them to the wall just under each side of the table. Gently push up on side of the table and put in one piece of wood flush along the wall and screw into place. Next, you need to push up on the other side of the table, with more force this time, and install the second piece of wood. That's it, sailors have jumped ship and your done....unless....If the table now wants to wander away from the wall, you'll need to put a couple of screws through the new pieces of wood and into the bottom of the table. Measure the new screws or you'll have them poking you in the elbow come dinner time. If you pre-drill those braces/pieces of wood, you should make it through the whole project without the slightest tinge of blue air.
"If everything seems to be going well, look around, you've obviously overlooked something."