The clue suggests to go to the "FRIDAY SQUARE NUMBERS" you found in the last part. Specifically, go to Friday Puzzles 1, 4, 9, 16, 25, ..., 121.
There are some unusual aspects to the text of each of these entries that form a marked path. This consists of single bolded words in the odd square entries saying "LOOK AT THE TIMES THESE POSTED", and single underlined words (originally "blinking" words but while that was very clear on some browsers, it isn't a universal html tag and was invisible on others) in the even square entries that say "GET RID OF THE ROOT".
As indicated in the flavor-text, a 24-hour clock should be used and minutes after midnight is the critical value. This gives 23, 18, 42, 56, 25, 108, 14, 144, 45, 10, 121. The time for the (n^2) entry is always a multiple of n, and "GET RID OF THE ROOT" here means to divide by n to get 23, 9, 14, 14, 5, 18, 2, 18, 5, 1, 11 or WINNER BREAK. Submitting this answer ends the hunt, giving the solver a deserved break from any more of these puzzles. For those who saw a slight connection back to the typos in the first part, I also accepted (with correct rationale), WINTER BREAK, a generic term that describes the holiday period in school calendars in the US.