He had to have also signed a DD Form 149, Application for Correction of Military Records, in order to be eligible for review. If he was successful, and it looks like he was, then that Form, along with all other records of the proceeding, is sealed.
Start from now and try to follow a paper trail backwards. Microfiche was the common storage method back then for these records, so there may not even be any actual physical documents left to get at.
Here's 10 U.S.C.S. 1162 and 1163.. Both have since been repealed in 1994. Note 1163.
§ 1162. Reserves; discharge
(a) Subject to other provisions of this title [10 USCS §§ 101 et seq.], reserve commissioned officers may be discharged at the pleasure of the President. Other Reserves may be discharged under regulations prescribed by the Secretary concerned.
(b) Under regulations to be prescribed by the Secretary of Defense, a Reserve who becomes a regular or ordained minister of religion is entitled upon his request to a discharge from his reserve enlistment or appointment.
10 USCS § 1163 (1992)
§ 1163. Reserve components: members; limitations on separation
(a) An officer of a reserve component who has at least three years of service as a commissioned officer may not be separated from that component without his consent except under an approved recommendation of a board of officers convened by an authority designated by the Secretary concerned, or by the approved sentence of a court-martial. This subsection does not apply to a separation under subsection (b) of this section or under section 1003 of this title [10 USCS § 1003], to a dismissal under section 1161 (a) of this title [10 USCS § 1161(a)], or to a transfer under section 3352 or 8352 of this title [10 USCS § 3352 or 8352].
(b) The President or the Secretary concerned may drop from the rolls of the armed force concerned any Reserve (1) who has been absent without authority for at least three months, or (2) who is sentenced to confinement in a Federal or State penitentiary or correctional institution after having been found guilty of an offense by a court other than a court-martial or other military court, and whose sentence has become final.
(c) A member of a reserve component who is separated therefrom for cause, except under subsection (b), is entitled to a discharge under honorable conditions unless--
(1) he is discharged under conditions other than honorable under an approved sentence of a court-martial or under the approved findings of a board of officers convened by an authority designated by the Secretary concerned; or
(2) he consents to a discharge under conditions other than honorable with a waiver of proceedings of a court-martial or a board.
(d) Under regulations to be prescribed by the Secretary concerned, which shall be as uniform as practicable, a member of a reserve component who is on active duty (other than for training) and is within two years of becoming eligible for retired pay or retainer pay under a purely military retirement system, may not be involuntarily released from that duty before he becomes eligible for that pay, unless his release is approved by the Secretary.
They still store certain parts of your military record on microfiche, not all but most. However they're suppose to archive your originals upon discharge. Is the system perfect? Nope.