(the below, obviously, is to the best of my understanding!)
There are two types of eligibility here, confounded by the COVID changes. Ivy League eligibility says that if you are enrolled in school, your clock is ticking. Period. NCAA rules say that your clock doesn't tick if you are enrolled but not officially competing (red shirt). Both say that your eligibility starts when you first enroll in college, and I believe you have a year after HS graduation to matriculate to college. Cornell (and increasingly the other Ivy League schools) have the "grey shirt" in which a student defers matriculation for a year and trains with the associated RTC; sometimes the student has *not* yet been admitted and takes classes nearby to improve their chances. The latter case apparently is also to keep up the statistics of admitted freshmen, since a deferred admission can count as a "transfer," or something like that.
Both NCAA and the Ivy League had the "four out of five" rule, by which a student has five years to use up four years of eligibility. So a red shirt allowed a non-Ivy student to stay in school and not lose eligibility. An Olympic red shirt for an Ivy student means the student was not enrolled.
Because of COVID, the NCAA and the Ivy League changed that rule to "four out of six," thereby allowing an extra year of eligibility for those who lost a championship year (or in the case of the Ivy League, a whole f***ing year of competition). I believe but am not certain that an ORS does not count towards that "six": if it did, then nobody would be able to take more than a red shirt year and one ORS and still have eligibility.
Vito: HS senior, grey shirt, Cornell freshman (year 1), Cornell sophomore (2), ORS (3), COVID year (4), Cornell junior (5). It is also not clear to me that the Ivy League would allow Vito to take an ORS (6) *and* a Cornell senior (7!) year. That would also put him at age 25 or 26 that last year. It is possible that the Ivy League would grant him a leave of absence (which is what an ORS in the Ivy League actually is). In fact, since the Ivy League doesn't allow grad students to compete, guys have been known to sit out the fall semester so as to not graduate before their NCAA eligibility is used up.
Crazy stuff, made more complicated by the Byzantine Ivy rules and that COVID thing.