A non-fly day can end at any point time of the day. Starting your first day of LC is easy math because you start LC at 0000 so the earliest you can report is 10 hours after that as long as the assignment is made by 12 hours prior to the start of LC. But those rules apply to any non-fly day end time. So in your case if you were legally assigned a 30 hour rest period that ends at 0600 then the earliest you could be made to start a rotation or SC is 10 hours after 0600 (so 1600) as long as the assignment is placed by 12 hours prior to the start of LC (so 1800 the day prior). The only time you are required to check your schedule is within 30 minutes of blocking in on the last leg of a rotation. So you are not required to check your schedule at 1800, 12 hours before starting LC, although most people would recommend doing so in order to keep scheduling honest in case they try to pull some shenanigans. If no assignment is made by 1800 you continue to have no obligation to check your schedule, so the part I bolded in your post is completely incorrect. You simply start LC at 0600 the next day and should just wait for proper contact from scheduling for any future assignments.