Some of the best ideas and designs start on napkins. Might have been research/think time.
If I'm solving a problem for a customer in the shower, should I not bill for that time if I'm getting results (especially when I'm holding down two jobs, and my personal time is where I fit my second job)? Granted, I shouldn't be able to bill for all my shower time, but time specifically devoted to a customer, sure, it's legit.
I do some of my best thinking while sleeping (and prepping before going to bed) and usually piece it together in the shower. I just can't get much think time once I'm taking the kids to school or getting interrupted at my day job or in the evening until the kids get to bed.
If I want to write it down while at lunch on a napkin, that's totally billable. Granted, I only do so in quarter hour chunks and I keep accurate time.
Further, there is nothing wrong with double or even triple billing (beyond that, and I think you're going to be kidding yourself at your multitasking skills). Take for instance patching VoIP servers back Cisco CallManagers ran on Windows 2000 and required tons of reboots for the OS, SQL, CCM app, Security Agent, etc. Say I know it is going to take 1 hour to do the patching, and another 15 minutes prior going through my check lists, and 15 minutes post to verify everything is good. So if I have 3 customers that I'm going to patch in one night, so I do it serially or in parallel? I'm going to do it in parallel and triple bill some of that time. I start first pre-patching checklist, then patching. Then I do the second per-patching check-list, and patching. Finally I start the third pre-patching checklist, and patching. Time for a quick bathroom break and then time to start the post-patching check of customer 1, then 2, then 3. Sure, if I run into a snag with one customer I have to pause all the billing for the other customers, but that's on me, and it's also why we have redundant systems.
Yeah, that's how to do it. Customers each get billed 1.5 hours. Takes me 2 hours to do it total, I bill 4.5. Everyone gets what they asked for, I'm efficient with my time, win win.
Now, billing >24 hours in a day, that would take some gravitational time dilation, and even then I think it's only on the order of seconds, not hours more per day.