Hey @sticky-breakfast-99649 - it depends. Usually, with what I have seen - US companies generally follow an hourly rate pattern and European companies usually do days (or months).
I have, over time, strongly avoided hourly contracts as it is extremely stressful for the developer (us) - for the same reasons you mentioned.
Also, if you time yourself strictly (for an hourly contract), an 8h stint on the computer is roughly 12 - 14h overall.
You should atleast try to get the contract to be daily - if not weekly or monthly.
For when I have done hourly rates, the hourly charges have been ~ 2 - 3x of my hourly rates - if I did a daily contract.
For example, if you do a daily rate of $400 for an 8h day, the hourly rate could be between $100 - $150.
Though my hourly rates have usually been for short term projects (6-8 weeks) and I have not been in a situation where work is less - but other folks could advise who have more experience in hourly rates.
The previous company my wife worked with, she had a minimum billing hours per month - so minimum 80h / month in her contract which took care of times when there was no work. (You could adjust your hourly rate accordingly if they are willing to do a minimum hours thing). Hope this helps.