The video for this song was Henley's first as a solo artist (he appeared the previous year with Stevie Nicks in the video for "Leather And Lace
"). While it did show up on MTV, it got surprisingly few spins considering the dearth of videos the network had to choose from in the years after they launched in 1981.
Henley was an obvious choice for hot rotation, since MTV saw themselves as having a Rock format and was desperate for established American acts (videos had been popular in Europe for a while, which is where most of their content came from). Logistics may have been a problem, since MTV was in New York and Henley was based in Los Angeles, but it still seems odd that he couldn't get more time than A Flock Of Seagulls or Haircut 100. Henley didn't even make a video for "Dirty Laundry"; his MTV breakthrough came in 1984 with this clip for "The Boys of Summer