No it doesn't depend. This is the same mentality that charges customers in "picodollars".
How many hours a day you work has nothing to do with how many "hours a day" (ugh) you bill.
You, in particular, and an impossible consultant to find on the general market. For even the best-capitalized companies in the world, people like you do not exist. They are hiring PCI consultants from body shops to validate new cryptographic protocols. I know this, because I read the reports they give their clients before demolishing those same protocols.
I know a couple other people with the same portfolio of talent. They, too, want to work in sub-day increments. And they do. But they bill project rates, because they can.
You are billing yourself out like a graphic designer. Stop doing that. Or don't, but don't pretend like you're being clever about things for undercharging.
Interesting... you say I'm billing like a graphic designer; I think I'm billing like a lawyer.
To be clear, if someone calls me up and says "I want you to do 10 minutes of work for me", I'm going to say no. The sort of consulting I most enjoy is where I'm going to be doing 50+ hours in total, spread over many months. It's not project work; it's expert-on-call work, and if I had to quote a project rate every time someone wanted to ask me a quick question, they wouldn't ask quick questions.
A possible way to structure that business relationship is you have identifiable projects where Real Work gets done. You do the whole contract / invoice / etc song and dance for those, at project rates.
In between projects, you make it known that you are a friendly guy, and bending your ear for a few minutes is free. N.b. This is how lawyers will generally work. This is to maintain customer loyalty for the five figure engagements. Plus, since you're doing it out of the goodness of your heart, you have an instant, built-in non-excuse for unavailability.
In cases where I've been hired for an identifiable project, that's what I've done. But not all consulting fits that mould; the most interesting I've done has been in the category of "be available for random stuff we throw at you, and send us a bill at the end of each month".
