Q: Are there any records from the drafting of the 22nd which explain why the word "elected" was used instead of "eligible"?
TLDR: Both "eligible" and "ineligible" appeared in early versions of the proposed amendment. Senator Warren Magnuson thought the revised text using "elected" would be easier to understand and achieve what was really intended. Others agreed.
A summary description of the change is in: The Twice and Future President: Constitutional Interstices and the Twenty-Second Amendment, 1999.
- Proposal and Ratification of the Twenty-Second Amendment
H.J.Res.27 as originally introduced used "eligible".
[n]o person shall be chosen or serve as President of the United States
for any term, or be eligible to hold the office of President during any
term, if such person shall have heretofore served as President during
the whole or any part of each of any two separate terms.
The House Judiciary Committee revised H.J.Res.27 to read.
Any person who has served as President of the United States during
all, or portions, of any two terms, shall thereafter be ineligible to hold
the office of President.
Having passed the House, the resolution was sent to the Senate. The Senate Judiciary Committee then modified the language to read.
A person who has held the office of President, or acted as President,
on three hundred and sixty-five calendar days or more in each of two
terms shall not be eligible to hold the office of President, or to act as
President, for any part of another term.
Then, on March 10, the Senate
considered an amendment offered by Democratic Senator
Warren Magnuson that would have replaced the Judiciary
Committee's language with the seemingly more straightforward provision that [n]o person shall be elected to the office
of President more than twice." Magnuson explained that the
language in his proposal, unlike the "complicated legal
language" of the Committee version, "could be easily
understood by everyone, and... would not involve complicated
legal questions," such as "When is a man Acting President?
When does he assume the office" and, "to what period he
should be limited" when "elevated to the office of President
through circumstances beyond his control"? Magnuson
argued that his proposal would bypass these questions by
focusing on what was "really intended to be reached"-
preventing a President from "perpetuat[ing] himself in
office."
After further debate, the final language using "elected" was approved.
Senator Magnuson's address to the Senate is in the Congressional Record, March 10, 1947.
Addressing a comment:
During the Federal Convention of 1787, (July 17) the election, length of the term, and eligibility of the Executive (President) were discussed.
On who is to elect the president, the choices were National Legislature (Congress), the people, or "Electors appointed by the several legislatures of the individual states" (Electoral College).
On the length of the term, the choice was seven years, more or less, depending on whether the Executive is "re-eligible".
On "re-eligible", the choice was yes or no.
[Debate on] “For the term of 7 years” resumed
Mr. Broom was for a shorter term since the Executive Magistrate was now to be re-eligible. Had he remained ineligible a 2d. time, he should have preferred a longer term.
It is apparent that "re-eligible" was used as "able to stand again for election".
Citations:
Peabody, Bruce G. and Gant, Scott E., "The Twice and Future President: Constitutional Interstices and the Twenty-Second
Amendment" (1999). Minnesota Law Review. 909.
https://scholarship.law.umn.edu/mlr/909
The Records of the Federal Convention of 1787, ed. Max Farrand (New Haven: Yale University Press, 1911). Vol. 2.
https://oll.libertyfund.org/titles/farrand-the-records-of-the-federal-convention-of-1787-vol-2