All the guys were college football players back in the day. LBJ once deadpanned about a Speaker of the House, "Nice guy but he played football too long without his helmut on..." They were all friends and kidded each other.
Being only 6 years old when Kennedy was assassinated, I don't recall if I was ever taught is school, that the nation was without a vice president during that time.
I'm glad you brought this up. I love learning interesting things. It seems a little trivial now, but still interesting.
Before the 25th Amendment, there were about 12 Vice Presidents who died in office leaving the position empty until the next election, a situation apparently holding no historical significance. Also 5 vacancies due to promotion after the death of the President. It was bound to happen eventually that a President would die or leave office with no VP in line. The Nixon-Agnew situation would have been that event.