The '90s saw a quickening pace as Fleetwood Mac released five live LPs capped by The Dance, a five-million-selling smash that reunited the Rumours lineup for the first time in 10 years.

One of the tracks recorded that day, a cover of Chester Burnett’s “No Place to Go,” wound up on the debut album by the band that would be dubbed Fleetwood Mac. As with their other ’60s ...