Tommy Burns was manager of Killie between 1992 & 1994. He was a Scotland international, winning eight caps between 1981 and 1988, while a Celtic player. He very sadly died in 2008, aged just 51.
From his Wikipedia: Burns moved to Kilmarnock from Celtic, where he became player-manager in 1992, winning the club promotion to the Scottish Premier Division in season 1992/93. Burns moved to become manager at Celtic at the start of season 1994/95, in acrimonious circumstances as he was still under contract to Kilmarnock as both player and manager.
Kilmarnock refused to release him from his contract and the Scottish Football Association subsequently fined Celtic £100,000 for 'tapping', or speaking to Burns without obtaining Kilmarnock's permission. Kilmarnock were also permitted to retain his playing registration, effectively ending his professional career as a player.
At Celtic, his team grew a reputation for playing attractive and attacking football and they won the Scottish Cup in 1995; but Celtic proved unable to break the domination of Old Firm rivals Rangers. Burns signed players like Pierre Van Hooijdonk, Paolo Di Canio and Jorge Cadete, and while the Celtic team lost just one game in the league during the 1995-1996 season, they were unable to beat the Rangers team. Burns commented that "Andy Goram [the Rangers goalkeeper] broke my heart" would be on his tombstone. After losing a Scottish Cup semi-final to Falkirk, Burns was sacked from Celtic in 1997 and went on to work under Kenny Dalglish at Newcastle United. as a coach.