Toilet needs it's own vent pipe. You see them on roofs coming out. They are the vents for drain pipes.
Install one for your toilet.
What you call a sewer vent cap is actually where you connect the drain vent pipe up through the roof.
Since it is under the sink it is also the vent for the sink.
We call that incomplete installation.
If you do not like drilling holes in your roof, you can have it exit through the wall. Cover it with mosquito net to stop Lake monsters coming in. Then put a nice vent cap (vented) on it to make it look good.
