While Squier continued recording through the mid-1990's, he did not have a top 40 single or album after "Rock Me Tonight," making it an interesting and somewhat sad anecdote. And that would be the end of the Billy Squier story, except ...
Squier's trademark sound was punctuated by a driving beat, something that is particularly evident on his earlier work ("The Stroke," for instance). Bolstered by the superb (and loud) Bobby Chouinard, this strong backbeat would differentiate Squier's songs from many of his contemporaries. In fact, he led off his first solo album -- 1980's Tale of the Tape -- with a drum intro on "The Big Beat" (side 1, song 1).
Having a clean drum break proved to be irresistible to early rap acts, and the drum intro on "The Big Beat" was sampled as early as 1981. Over time, the enthusiasm for the drum line has not waned, and it has been used by artists including: Jay-Z ("99 Problems"), Run-D.M.C. ("Here We Go"), and Alicia Keys ("Girl on Fire'). As of this writing, "The Big Beat" has been sampled in nearly 200 songs, and is one of the 10 most popular samples of all time. Other Squier songs, particularly "The Stroke" are also popular samples.
Unfortunately, this popularity has not translated to a resurgence in Squier's career, and in recent interviews he seems someone ambivalent about the sampling. For readers who are interested, Squier's first two LPs -- Tale of the Tape and Don't Say No are particularly strong and well worth a listen.
I don't recall ever seeing the original video for "The Big Beat" on MTV back in the day, so it definitely qualifies are a rare (and cool) video. I'm not totally sure about the yellow pants, though. Also worth checking out: roller skates! (1:20) and an obscure Eraserhead marquee (2:30, but blink and you'll miss it).