This is very interesting. How do you handle working with multiple clients? E.g. I'm working on this project for this client, this week but the client from last week has an urgent question/issue that I need to look at. Would that be billed hourly, or as part of next week or something to that extend?
For work that actually requires me to crack open a terminal, it's as you described i.e. in the vast majority of cases it can probably wait until the next week they've booked. In the rare case that they're losing money thanks to inaction or if the problem is directly due to an error I made, then I'll fix the thing so that it's in a working state right now and work on a longer-term solution in their next slot.