I think clopen is too complicated in that it expresses ranges that are not practically useful, like (10,11], and it complicates expressing something like "Open 0-24", where your notation appears to require a date.

I think you get the essential utility you want in a 24 hour clock by simply letting 24 (or "24:00:00" when fully written out) be a way to represent the end of the day.

It's also already in use, with examples at https://ioi2023.hu/faq/ , http://www.garageferrarimilazzo.com/en/ , and https://jozsefvaros.hu/english/news-in-the-district/2022/12/... .