It's better to be not "available immediately" if you get a call.
The most offensive customer I ever had called and told me on the phone that he would "meet me at his house in 10 minutes." When I offered him a timeslot in a week or so, this dipstick questioned my credentials.
He also fell silent at intervals, hoping I'd fill the vacuum with something he could use. The silence has the effect of raising the tension.
I don't advise working for doctors or lawyers (or ambassadors, like this ^ one).