Brigham Young said, "Some of the Witnesses of the Book of Mormon, who handled the plates and conversed with the angels of God, were afterwards left to doubt and to disbelieve that they had ever seen an angel." (Journal of Discourses, Vol 7, page 164, 1859, Brigham Young.)
I have had the misfortune of watching close family members get involved with a religious cult where they were lead to believe that angels were talking to them and they were on a mission from on high. When one of them finally got out of the manipulative group he told me that he had allowed himself to be lead through imaginary visions that he believed were actually happening because he had been conditioned to do so by the group's leader (ie conman). Personally I believe that a very similar form of psychological conditioning occurred with the Book of Mormon witnesses.
As a result several of the book or mormon witnesses later went on to distinguish between seeing with "physical" and "spiritual" eyes, which could be very easily compared to the type of angelic visions that my family member was privy to when he was a part of a religious cult (unrelated to the Church of Jesus Christ of Latter-day Saints).
The following are additional facts about the Three Witnesses (with sources) where they make decisions using the same spiritual base they used to see the gold plates and the angel:
Martin Harris signed his name to a statement: "Testimony of three witnesses: We Cheerfully certify...The Lord has made it known to me that David Witmer is the man. David was then called forward, and Joseph and his counselors laid hands upon him, and ordained him to his station, to succeed him...He will be prophet, seer, Revelator and Translator before God." Signed Martin Harris, Leonard Rich, Calvin Beebe. Of course this never came to pass as Brigham young became Joseph Smith's successor.
Phineas Young wrote to his older brother Brigham Young on December 31, 1841, from Kirtland, Ohio: "There are in this place all kinds of teaching; Martin Harris is a firm believer in Shakerism, says his testimony is greater than it was for the Book of Mormon" (Martin Harris - Witness and Benefactor of the Book of Mormon, 1955, p. 52)
David Whitmer said in 1887: "If you believe my testimony to the Book of Mormon; if you believe that God spake to us three witnesses by his own voice, then I tell you that in June, 1838, God spake to me again by his own voice from the heavens, and told me to 'separate myself from among the Latter-day Saints...'" Address to all believers in Christ, p27, 1887
David Whitmer changed his story about seeing the plates and later told of finding them lying in a field and later still, told Orson Pratt that they were on a table with all sorts of brass plates, gold plates, the Sword of Laban, the ‘Director' and the Urim and Thumim. (Millennial Star, vol. XL, pp. 771-772)
During the summer of 1837, while in Kirtland, David Whitmer pledged his new loyalty to a prophetess (as did Martin and Oliver) who used a black seer stone and danced herself into ‘trances.'(Biographical Sketches, Lucy Smith, pp. 211-213)
In 1847 David Witmer declared to Oliver Cowdery that he (Whitmer) was to be the Prophet of the New Church of Christ and Oliver a counsellor.(Letter to Oliver Cowdery, by David Whitmer, Sept. 8, 1847, printed in the "Ensign of Liberty," 5/1848, p. 93; also see ‘Ensign of Liberty,' 8/1849, pp. 101-104)
As a Methodist, Oliver Cowdery denied the Book of Mormon (Times and Seasons, vol. 2, p. 482 and Improvement Era, Jan. 1969, p 56 and "Oliver Cowdery-The Man Outstanding," Joseph Greehalgh, 1965, p. 28)