Are the terms unknown arbitrary labels chosen for two chord types simply to be accepted, not thoroughly understood or, is there an exact historical account of who, when, where, and especially why, the terms major and minor were chosen to describe two chord forms?
The chords are named after their thirds. Major and minor are Latin for "bigger" and "smaller," and the major third is bigger than the minor third because it spans four semitones (originally understood as two whole tones) while the minor third spans only three (originally conceived as one whole tone plus one semitone). This understanding was in place at least by the 1480s, before "chord" was established as a theoretical construct. For example, John Hothby, who died in 1487, wrote in de arte contrapuncti
Disonantia tertia est duarum specierum, scilicet maioris et minoris. Disonantia tertia maior est formata duabus tonis, et tunc talis tertia vocatur ditona, sicut patet per exemplum. Disonantia tertia minor est formata uno tono et uno semitono, et tunc vocatur talis tertia semiditona, sicut patet per exemplum.
This means
The dissonance of the third is of two types, namely bigger and smaller. The bigger dissonance of the third is formed of two tones, then such a third is called a ditone, as may be seen from the example [which is unfortunately not reproduced in the linked page]. The smaller dissonance of the third is formed from a tone and a semitone, then such a tone is called a semiditone, as may be seen from the example.
From another treatise of the 1400s:
De tertia maiori et minori -- De tertia cum quinta
Item due sunt tertie scilicet maior et minor. Maior autem uocatur tertia ditonalis, [...]
De tertia cum vnisono.
Item tertia minor dicitur tertia semiditonalis [...]
And here's an anonymous source that names pitches for good measure:
Duplex est tertia, scilicet major et minor. Major est ditonus qui fit ex duobus tonis. Sicut ut mi, fa la, et e converso mi ut, la fa. Tertia minor est qui fit ex uno tono et uno semitonio minore, sicut de A ad c, et de [sqb] ad d, et de d ad f, et de e ad g, et de g ad b, cantando fa supra re, vel e converso, vel sol, supra mi, vel e converso, et vocatur semiditonus.
Translated:
The third has two forms, bigger and smaller. The bigger is the ditone, which is made of two tones. Such as ut mi, fa la, and the other way around mi ut, la fa. The smaller third is the one made of a tone and a smaller semitone, such as from A to c and from B natural to d, and from d to f, and from e to g, and from g to b flat, sung as fa above re, and the other way around, and sol above mi, and the other way around, and called the semiditone.