I have a client that wants to forward his calls to me when he's busy with a meeting. He wants me to be available from 9-5, but will only be forwarding his calls to me when he's with a client. Do I bill him for the entire time he may be forwarding calls or just for the time I'm on the phone? There may only be 5-10 calls a day, so I won't be on the phone much, but he doesn't want the calls to go to voice mail.
If I have a client that wants me available during a specific span of time, they pay for that time. How they utilize my skills in that time is their option.
They are free to schedule and pay for 8 hours, and ultimately only utilize my skills for 30 minutes. They still pay for the 8 hours they requested I be available to them.
Like all my clients, they pay for my time and experience. I'm not really paid for just completing manual tasks. Any schlub can perform manual tasks. It's the knowledge and experience I posses that makes my performance worth my rates.
This is basically a contractual matter and depends on the type of work (mission critical or mundane support) and your client's expectations.
Generally, clients pay for your time - so it depends on how much of a burden being on-call is. If it actually prevents you from performing other work, it would need to be compensated as actual work. However, if you need not react immediately and can still plan your working day as you see fit, some sort of discount could be given.
Billing for non-worked time (from the client perspective) can easily sour a client relationship - so the agreement needs to be concrete and in writing.