According to Michael Krogsgaard's research (see link in Appendix F) this session was specifically for overdubbing "4th Time Around", and the musicians involved were Kenny Buttrey (drums) and Charlie McCoy (harpsichord). There is clearly no harpsichord on the released track, but it's quite possible that the harpsichord idea was dropped before the final complete take.  Michael Krogsgaard states (incorrectly, I believe - see Part I) that this session took place after the release of  Blonde On Blonde, and that the overdubbed track was never released; but this could be Michael's inference from the fact that no version of the song containing a harpsichord has ever appeared.

It's certainly clear that the overdub was done fairly late in the production process, as at least two mono mixes and one stereo mix had already been made prior to this.

Furthermore, if the overdub was not intended for use on the album, then we lack an explanation for why the session was held at all.  The only other conceivable reason might have been that "4th Time Around" was being considered for release as Dylan's next single; but no such suggestion has ever come to light.