Paul Languedoc worked for Time Guitars in the early 1980s, before he became the sound man for Phish in fall 1986. While at Time, Paul built at least two custom guitars for Trey Anastasio of Phish that I know of. His famous hollowbodies for Trey came later.
The first Time guitar Paul built for Trey was a mini travel guitar. You can hear it on early Phish live tapes, sounds a little like a mandolin.
The second, delivered in spring 1986, was a Strat-style guitar with a solid walnut body. It had tremendous tone and sustain but was heavy as hell.
The Time guitar on ebay, however, cannot have been a Languedoc if it's ca. 1979. Paul was in college in Maine at the time. He graduated in 1981.
But the ebay example clearly shows that Paul was influenced by his time at Time. Note the binding in particular.
No Alembic connection I'm aware of.