Uh, the most obvious one: coincidence? They were both elderly, and it's not unlikely from a statistical standpoint that they'd die with the same time-frame (as contemporaries do, esp in that time period where there likely was less variability in lifespans for their common socioeconomic level).
The easiest explanation IS that it was a coincidence, such will be enough for the rational mind. However you didn't explain why Adams said, "Thomas Jefferson lives" right before he died.
Furthermore, there's a well-known phenomena of those who are close to death or fighting terminal illness being able to hang on to witness an important event (witnessing the 50th anniversary of the U.S. is not an unreasonable thing to think they'd share, and wish to see before they "let go", being that it's such a sentinel achievement of both of their lives). This is a well-known phenomena amongst hospice workers and medical professionals that people can somewhat control the time and day of their death, where they just give up emotionally and quit 'fighting'.
Just because it's well known doesn't mean it's explained. The fact that Adams and Jefferson died in the manner of which they did is extremely remarkable. I know you don't disagree with this.
Occam's razor says
So, what this means is that you lack a suitable explanation for the event and have to lean on the philosophy of William of Ockham. In the analogy the sheep are going missing, but the explanation is lacking. We know that they are disappearing so we know SOMETHING is happening we just don't know how. This is exactly the explanation you used with Adams' and Jefferson's death. You know that they died in a remarkably mysterious manner, but the how is not well understood. You know that others can die in this way too, but that's just like saying that other sheep have gone missing too. It's NOT an explanation it's just an admittance of reality which is merely the observational stage of the scientific method. You can't call it science until you get to the end of the method. You have to call it something else.
So your explanations are "coincidence" and "Occam's Razor." You didn't give any spiritual explanations and there are many that fit (the soul and reincarnation for example) even though I explicitly requested that you do. You are perfectly content with a non explanation which fits perfectly in my analogy.
Lets say you have sheep too and your friend is the one that has his going missing. You don't have the motivation to solve the mystery of the disappearing sheep because you have no personal investment. However, if the same thing started happening to YOU, would you merely call it an unsolved mystery? No, you would do everything in your power to save your livelihood. You wouldn't be content with the explanation, "sheep go missing every now and then" because if you set your watch to that you'd eventually go bankrupt.
The people on this planet are largely spiritually bankrupt. They see the evidence, but they are not interested in pursuing because they gave up their spiritual bank account number to William of Ockham.
People die.
"Sheep just go missing every now and then, it's just a part of life."
-Sab