I have some small ideas of how to test one but they are pretty "home-made" and I do not know of a real test as dealers often just replace, rather than test.
First we might talk about the how and why these gizmos are there as they are so simple but so tricky!
We have a trap under most sinks and lavatories on the Rv just as we do at home but on RV we don't find it good to make lots of vents through the roof like we do at home, so they use these air gaps more often. At home they just run a small pipe up and out the roof!
I made a drawing of how the trap and air gap are supposed to work.
When we run water, there is a certain amount designed to stay in the loop at the bottom called the trap. This water filled trap acts as a plug to keep odors and dangerous gas from coming into the house from the sewer. You can see it in the bathroom stools as the standing water so imagine the same at each sink, vanity, etc.
When water flows down the pipe as we flush or drain the sink, it can create a vacuum as it goes down the pipe as this vacuum can draw all the water out of the trap, leaving it open to let gas smell into the house. But to keep that vacuum from drawing the water out of the trap, we add a vent on all pipes in this situation. I've drawn this vent mechanism as a green line on the drawing, just to make it simple to imagine.
Normal operation in RV is that the flap opens easily to let air go in the pipe to relieve the vacuum and leave water in the trap. Works fine most of the time and if you crawl in under the sink or vanity to look up at the pipes, you may see this as a small section of "pipe" glued on the top of the upright drain pipe.
BUT two things can happen to the airgap. One is that it sticks OPEN and lets gas and odor come back up the pipe, through the vent and we smell it!
Two is that it may stick CLOSED and that lets the water falling down the drain create enough vacuum that the water sealing the trap is also pulled out, leaving an open path for odors to come up, through the trap and inside!
Both of these situations depend on lots of variables like how much water draining, how long the drain, what angle, etc, ect. but they can happen pretty easy with a small (cheap?) plastic gizmo, so it may need checking.
This is technically more correct to be called an "air admittance valve" when shopping and this is a link to one to show a number of things. Like how easy it is to change if it screws in, but I expect them to be glued!
https://www.amazon.com/Oatey-39012-...ocphy=9028263&hvtargid=pla-305607402370&psc=1
Testing? One way is to cover it with something like cling wrap to rubber band a solid seal over the vent to see if the odor stops and also to make sure there is water standing in the trap before taking off to drive. The water can sometimes be slopped out of the trap it we get into steep, wild driving!
If we are stopped and setting AND if we are lucky enough to have a drain plug which holds water long term, we can fill the basin with water. Then it is trial and error to see what stops the problem.
But if you are lucky enough to find it is only screwed in, changing a $3-4 item may be the better way to go?
IF you are a DIY person, cutting the pipe and old gap out to replace it with a pipe fitting so the next one can be screwed in is a good move. One of the new little oscillating tools is great for working under sinks to cut pipe.