Thanks for the drawings, clear now, the other side of the wall is the same tile but their is also a toilet there in the way.do not know what is on the other side of that wall...you may be able to cut sheet rock in a bedroom or closet. instead of tile.
work it from the other side
Yup I see that as well, and thanks to everyone that has contributed to this post.Vents are connected on the waste side of the p trap as opposed to the fixture side. They typically run up to the attic, connect up there and then up and out through the roof in a much larger pipe. Some vents can and will go up over and down to connect into another pipe using it as a vent. There are also wet vents and automatic air vents. For your purposes, you need to fix what was done incorrectly by opening the wall up and replacing a couple/few tiles. You don't need to tear apart your whole bathroom. A repair like this would typically take about 4 to 6 hours if you have all the parts on hand and voila!
No more flies.
Summer is coming; it will only get worse.