Well, the Presidential age of eligibility requirement has never been put to the test, Constitutionally, but my interpretation is that the President has to turn 35 before being sworn in. So, if he were 34 on Election Day, he would still be eligible to take office as President as long as he turned 35 by Inauguration Day, January 20th.
It would be interesting to see it put to the test, however. The age of eligibility for a United States Senator is 30 years old, according to the Constitution. However, here’s where things get tricky: the Senate itself is the only body which can decide the qualifications for admission of its members, not the Supreme Court or judicial branch. This has resulted in three Senators (Henry Clay, John Eaton, and Armistead Mason) serving before they turned 30 (Clay was 29 while Eaton and Mason were 28). Those three underage Senators took office early in 19th Century, and while there is no evidence that they weren’t aware of their exact age, it wasn’t surprising for many people of that time to have no record of when or where they were actually born.
In more recent times, we’ve seen Senators elected before they were Constitutionally eligible, including Joe Biden, who was 29 years old when he was first elected in November 1972, but he turned 30 a couple weeks after Election Day and was Constitutionally eligible when he was sworn in.
We don’t know exactly how a Constitutional test of the Presidential eligibility requirements would turn out, and as is the case with many of these “what-if” scenarios, it would probably be ugly and messy and overly partisan. Any of the above actions are possible, but there’s also the case of U.S. Senator Rush Holt of West Virginia. Like Biden and Clay, Holt was 29 years old when he was elected to the Senate. Unlike Biden, Holt didn’t turn 30 before his inauguration, and, unlike Clay, the Senate didn’t seat Holt before his birthday in June 1935. The Senate DID, however, hold Holt’s seat for him until he was old enough to occupy it.
Now, that could never happen with the Presidency because there can’t ever be an interregnum, but if a candidate was elected in November and wasn’t Constitutionally eligible to hold the office until, say, April, would he be out of luck and disqualified from that election cycle? Would the Vice President-elect be inaugurated on January 20th and assume the office under the 25th Amendment (like the VP does when the President has surgical procedures which require anesthesia and is temporarily unable to discharge the powers of the Presidency) until the President-elect turns 35 and is Constitutionally eligible to assume office?
There are lots of unanswered questions and “what-ifs” and at some point we’re probably going to have to answer some of them. Believe me, I run some of these scenarios through my mind and start pulling out my hair when trying to come up with the correct answer without falling down more Constitutional rabbit holes. It’s such a weird thing trying to form a more perfect union out of such an imperfect document.
As for the last part of your question, whether it is An Unfinished Life: John F. Kennedy, 1917-1963 (BOOK•KINDLE), or one of his two volumes on LBJ — Lone Star Rising: Lyndon Johnson and His Times, Volume I: 1908-1960 (BOOK•KINDLE) and Flawed Giant: Lyndon Johnson and His Times, Volume II: 1961-1973 (BOOK•KINDLE) — you cannot go wrong with Robert Dallek. His recent book, Nixon and Kissinger: Partners in Power (BOOK•KINDLE), is a fascinating look at two of the most influential figures of the 20th Century, particularly when it came to foreign policy and international relations. Dallek also wrote a short, concise book, Hail to the Chief: The Making and Unmaking of American Presidents, which looks at how the Presidency has worked since McKinley modernized it at the end of the 19th Century and beginning of the 20th.