After becoming a big club act, Drivin' n' Cryin' signed with 688 Records in 1986; their first LP soon followed. Island Records then picked them up which led to some rock and college radio airtime. However, although they developed a loyal following, they never quite crossed over to mainstream rock audiences. Not only was southern rock out of favor in the late 1980's, but the shifting scene (from hair metal to grunge) made the late 1980's and early 1990's particularly treacherous for rock acts.
"Honeysuckle Blue" is off the 1989 LP Mystery Road. I don't recall ever seeing the video on MTV, although the song did pick up some radio play. However, neither the song nor the album charted.
Drivin' n' Cryin' would continue to have modest success through the early 1990's, and remain together as of this writing as a working band.