Hi, welcome to the forums.
They are capable of taking falls. There are the unfortunate falls but 9.999 times out of 10 they escape with no injuries.
At a young age and heck sometimes all the through there life they are somewhat shy. Your kid is new. Its best to put the cage up high in the room for now and only visit the cage when neccessary. I know it is hard not to want to go look at him or her but you have to restrain yourself right now. Let him get acclimated and then start presenting yourself a tad more with time.
Please fill this out so we can be sure he will acclimate as fast as he will allow.
https://www.chameleonforums.com/how-ask-help-66/
Chameleon Info:
• Your Chameleon – He is a 2 month old male Veiled Chameleon. He’s been in my care for 4 days now.
• Handling – Once or twice a day he is handled.
• Feeding – I’m feeding him 5 to 7 crickets every day. I put them into a small bowl in the bottom of his cage so that he can eat them as he pleases.
• Supplements - What brand and type of calcium and vitamin products are you dusting your feeders with and what is the schedule?
• Watering – I’m using a homemade drip system as well as misting several times a day. I do not mist until the cage and foliage is dry as to not promote URI. I see him drinking multiple times a day.
• Fecal Description – fecal matter is light brown with white urine. It is fairly solid but is moist. I haven’t had him tested for parasites, he may have been by the breeder but if so I was not informed.
• History- All the history I have is that he is 2 months old and a male. I was told by the owner of the pet emporium that he was bought from a reputable breeder.
Cage Info:
• Cage Type – His cage is glass with air vents underneath the door as well as a screen top. I will be getting a full screen cage ASAP!
• Lighting – Not sure what brand the fixtures are. For the heat bulb I have a small halogen fixture with a red bulb in it. That stays on 12 hours a day. The UVB bulb is in a 5x5 fixture and that is on 10 hours a day.
• Temperature – The basking spot is 87 degrees Fahrenheit and the lower half of the cage is about 82 degrees Fahrenheit. The lowest over night temp is 77 degrees due to having our thermostat set at that temp. I measure these temps with a combo thermometer/hygrometer.
• Humidity – Humidity levels are 50-55. I maintain these by misting to keep him hydrated, seems to keep them where they should be. I use a combo thermometer/hygrometer to measure humidity.
• Plants – No live plants, only artificial foliage.
• Placement – The cage is located in the living room of our house. Its approximately 5’8” off the ground. It is several feet away from the air vent that pumps out the warm air from our heater that is run by a set schedule on the thermostat.
• Location – I am located in Central California. Near the Yosemite National Park.
Current Problem – My concern is that he fell from his basking perch yesterday. He doesn’t appear to be hurt, has gone about his business as per usual with no problem. Also, I want to be sure these conditions are okay, I’ve read a lot about respiratory infections and I don’t want my new baby to get infected. I will soon be moving him into all screen cage large enough for him as an adult.