If I'm not on "my own time," I'm billing. I don't give a damn if I'm twiddling my thumbs because I'm bored.
I mean, I've worked in "support" roles where I would spend many days with a client doing nothing but sitting in a chair for 8 hours a day. Ultimately, it comes down to the fact that you are compensated for your time. It's not my problem if the client doesn't give me work to do.