‘The Mike Douglas Show (1961–1982)
Episode #5.91
Comedy, Music, Talk-Show | Episode aired 10 January 1966
Janet Blair is co-host. Guests are folk rock duo Simon and Garfunkel (“The Sound Of Silence,” “You Can Tell The World,” “Mr. Tambourine Man”); double-talk comic Al Kelly; and exercise expert John Hills’.
Paul Simon - 'Time it was...it was' 
‘The Mike Douglas Show (1961–1982)
Episode #5.91
Comedy, Music, Talk-Show | Episode aired 10 January 1966
Janet Blair is co-host. Guests are folk rock duo Simon and Garfunkel (“The Sound Of Silence,” “You Can Tell The World,” “Mr. Tambourine Man”); double-talk comic Al Kelly; and exercise expert John Hills’.
SOURCE: https://www.imdb.com/title/tt8566930/
I found ‘an unofficial video’ of this performance:
This video has been uploaded on July 5, 2020
‘ Complete appearance by Simon & Garfunkel on the Jan. 10, 1966, Mike Douglas Show’:
Wonderful! What great find this is. And 2 songs I never heard them play before on a show. Thank you for this link.