At the end of every evening or weekend work session on one of my project cars, I have a little ritual I follow. Once I have cleaned up my tools and put everything away, I like to just sit on a stool and study what I have done. And while I do not care to drink while I work on …
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My work is with structures and not automotive restoration (Yet), and your points fit well for me too.
If it is thinking time for a new problem I simply haven't yet faced, it is treated as educational time for myself and the client isn't charged. If the thinking and problem-solving time is because of the failed effort of a client or a previous "technician", then the time is charged.
Shopping time under 30 minutes is not charged and shopping time at more than 30 minutes is charged.
In my experience, thinking happens at many points; before starting the work, during the work, during breaks in the work, and after the work.
It seems the distinguishing factor of money flow for thinking and problem-solving is whether or not the problem is common enough to be reasonably understood early or if it is a matter of cleaning a mess.
Finding a needed part of which there seems to be only three in the world counts in the latter and billable condition.