After forming The New Monks in late 1980, Peter Tork recorded several demos in 1981 for Sire Records (a venture that was ultimately unsuccessful in landing the group a recording deal). "Since You Went Away" was written by a friend of Peter's, Michael Levine, and was one of the tracks demoed. Check out the New Monks' take on it below, courtesy of the Live Almanac's YouTube channel.
This song was later recorded and released on the 1987 Monkees album, Pool It!
Peter was doing some interesting things during this time period, both with the New Monks and The Peter Tork Project. An early '80s solo album by Peter, pre-Monkees reunion, very well might have been an interesting listen.
I've often wondered if Peter brought in a lot of songs from his New Monks/Project time period during the sessions for Pool It! The album's producer, Roger Bechirian, had this to say in an interview years after the album had been recorded:
"You know who was good? Peter Tork was an amazing multi-instrumentalist. I had no idea! He had a bunch of songs that would've made a great album. But of course they wouldn't have it - Jones wouldn't have it. Peter was great. I was really, really taken with him. He was full of life and had loads of ideas."
Monkees Farewell Tour