I must say that we are out of inspiration here about <style> name.
Anyway, we've built a new beta http://beta.plantuml.net/plantuml.jar that add background change for timeline.
Here is an example of what you can get:
Project starts the 2020-12-01
[Task1] lasts 20 days
sunday are closed
[Task2] lasts 40 days
[Task2] starts 10 days after [Task1]'s end
-- Separator title --
[M1] happens on 5 days after [Task1]'s end
-- end --
Syntax for background was easy.
Since you want to style months, day, weeks, I am not sure about the right option for styles.
Do we have to add "Day", "Month", "Weekday", "Year" ? And don't forget that some days may be closed.
And that you can change the printscale.
It would really help if you could help us to find the right syntax for style.