This passage clearly has Jesus Christ as its focus. He is said to be the King of kings and Lord of lords. He is said to be the blessed and only Sovereign. Christ alone possessing immortality and dwelling in unapproachable light refers to His mediating the divine glory. Paul thereby equates Jesus with God Himself. Christ is life. He furnishes us with life. Steven J. Cole gives the following commentary on 1 Timothy 6:13:
"I charge you in the presence of God ... and of Christ Jesus” (6:13). The close association of God and Christ Jesus, plus the assumed omnipresence of Christ, point to Jesus’ deity. Paul reminds Timothy that both God the Father and Christ are listening in and watching as he gives this charge to Timothy. Keeping in mind the fact that God and Christ are always with us will motivate us to live each moment to please Him, whether or not anyone else is there."
Interestingly enough, the Jehovah's Witnesses Watchtower Society agrees that 1 Timothy 6:15-16 refers to Jesus Christ:
"Jehovah and Jesus Christ. Jehovah is “the happy God” and his Son Jesus Christ is called “the happy and only Potentate.” (1 Ti 1:11; 6:15)."
If folks like the Jehovah's Witnesses want to admit that Christ is the object of emphasis in 1 Timothy 6:13-16, then that leaves them with the dilemma of having to explain how Jesus could be King of kings and Lord of lords. There cannot be two different figures occupying this same position of authority. The only logical and consistent explanation is that Jesus Christ is God incarnate.