Judging from his guitar here, it is almost certainly a lipstick tube unit or a Tele neck unit...
While this Wikipedia article concludes that it is in fact a Danelectro Lipstick Tube unit...
Guitars
Throughout his career Verlaine has played a variety of Fender guitars. Most famously in the heyday of Television he played a Fender Jazzmaster and a Fender Jaguar through Fender and Vox amps. These guitars were an unusual choice for a rock musician at that time. Verlaine is pictured inside the compilation The Miller's Tale playing both types of guitars. Recently, at solo concerts and at Television concerts, Verlaine has played a Fender Stratocaster, including one that has been modified with Danelectro pickups. He has also been seen using a standard Fender Telecaster with a rosewood neck in a video where he tries to teach Richard Hell the song "Venus" (though this was probably just a guitar owned by the studio they were in). Verlaine is credited as being instrumental in bringing what was seen as a "surf" guitar into the rock arena.
