12:21, mirror hour
Twelve twenty-one: 12:21. The digits of the hour, one and two, appear reversed in the minutes, two and one. A four-digit palindrome that occurs just past noon, the day folding back on itself in miniature at its central crossing point.
Six once more, and in six what goes out tends to come back. The palindrome draws it plainly: same digits, opposite order, the afternoon answering the morning. Just past noon you are early enough that most of the answer is still on its way, and late enough to have sent something out.