On our 1989 E38-200 there were three vents on the STARBOARD side of the transom, outboard just under the gunnel - fuel tank, CNG tank, and holding tank.
We once had the holding tank back up when the vent got plugged. What we found was that the vent had a fire-arrestor screen on it that was blocked with debris, and just removing the screen solved the issue.
After that it became a regular maintenance item to check the holding tank vent line for plugging. My method was to splice into the middle of the vent line between the tank and the transom vent, and then use a hand held Parr pump to pump water first in one direction, and then the other. That way I was sure it wasn't plugged at the transom end by spiders, or the tank end by a splash of solid waste.