Welcome to the forum!
A future herpetologist--that's great--- and you're smart enough to be asking questions before your cham is in serious trouble.
You'll see by my avatar that I have a male Jackson's ---one who doesn't enjoy being the subject of photos, hence the stress pattern on him.
You already know that gaping can be a sign of a respiratory infection or overheating.
The fact that your cham sits by the door waiting to come out leads me to suspect that it's hotter in his home than he can bear.
I have a Fischer's cham (also a montane type) who was overheating while being shipped.
So strong was his desire to escape the heat that he pressed his face against the shipping container for so long and so hard that his horns are permanently bent to the side
As for measuring temperatures in the basking spot, unless the thermometer reading was taken directly below the basking lamp an inch or two directly above the branch or vine where he sits, it will be much hotter than you would think.
Jackson's come from mountainous areas, so they can't tolerate the higher temps that many other cham species require.
Please be aware that Jackson's also cannot tolerate the significantly higher amount of supplements that other, non-montane species need.
It's a tough balancing act trying to keep enough humidity, while allowing for enough airflow to ensure a healthy cham.
Until you get a free-range area going, you can always increase the airflow in the terrarium by opening the doors or even just one door and affixing a towel to the opening with duct tape or similar.
It may not look pretty, but it will definitely increase the airflow.
The one sad fact about chams is that they stress easily and, being solitary animals in the wild, they are stressed by being handled.
I would love to hold my chams and have them sit on my arm, shoulder or head, but I want them to thrive and have long lives, so I resist the temptation.
Captive bred Jackson's are very seldom found on the market, so the seller may (or may not) have been selling a story as well as chameleons.
Hope this helps you out.