From the ADCHAM site..."Indigenous to the southwestern coastal regions of Saudi Arabia and western Yemen, the veiled chameleon occupies the wadis and agricultural lands of this otherwise arid region. "...so I don't think it should be like a desert there.
I've seen a few pics of the natural habitat some time ago and it didn't look like a desert at all. Everything was green with a lot of bushes and smaller trees.I also seen a pic from the edge of a desert-like area,a male sitting on the only stick reaching out of the sand...
People can make some reasonable deductions based upon known information.
for example: the dew licking to obtain water, the requirements of a certain amount of moisture for egg incubation ...etc.
While most people are thinking "lawrence of arabia", I would suggest a semi arid environment
where valleys and ravines would hold in much moisture in a micro-environment.
could be wrong..even up in the dry mountains where they cultivate coffee and khat.