How do I set my open hours to go past midnight?

A library is considered open on a particular day if an open period begins on that day, not if an open period extends to that day.

For example: Library is open 08:00am - 02:00am Monday - Friday but closed on Saturday and Sunday. The system interprets this as 08:00 am Monday through 02:00 am Tuesday, then 08:00 am Tuesday through 02:00 am Wednesday, etc. However, the library is open Tuesday because of the 08:00 am starting time, not the 02:00 ending time. The library would therefore be open on Friday but closed on Saturday, when there is no start time.

Please see how to generally configure open hours.