I brought the whole cage set up to my cottageIf a chameleon only gapes while under the basking light it likely has to do with its basking. Temperature may be to hot or it may be that the chameleon is hot and not moving to get away from the heat.
If it's gaping in other areas of the cage then you need to figure out if it's a URI. If it's saliva is stringy in this case, that might also be an indication of an RI.
Having the cage next to the window in winter in the area you live in can lead to an RI from the chill that the window produces.
Taking the chameleon to the cottage in the car...you would need the car to be almost warm enough that you would want to take your coat off.
At the cottage the cage needs to be away from the window too and not in a draft. Did youngster it's cage and lights and all with you to the cottage?
So I just redid my cage and my little thermostat isn’t the best so I didn’t put it back in. But I did make it the proper height. I can put it back in and see but I don’t know how accurate it really isYour chameleon looks a little small to be producing eggs yet.
I would move the cage away from the window.
What is the basking temperature where the chameleon sits in the branch?