Another way to think about it is that the -n takes the place of on Thursday.
It's one of the other uses of the accusative; it can show a measurement or a point in time: https://lernu.net/en/gramatiko/akuzativo#tempopunkto
Jes kiel en la plejparto de la lingvoj. Actually capitalizing day names is a peculiarity of the English language.
Many (but not all) speakers make the following distinction:
- ĵaŭdon - (on) Thursday
- ĵaŭde - (on) Thursdays
Even among speakers who make this distinction, not all treat it as a hard and fast rule, so always pay attention to context.
My sense is that either one would work... even in English:
- Can they come this Thursday?
- No, they're not available Thursday(s).
Personally, I would prefer ĵaŭdon in this context because it more clearly expresses the idea of "this one particular Thursday that we're talking about."
Thank you very much. You have helped me many times and I do not often say thanks but I do want you to know that I appreciate your help very much.