Leaders cannot engage people. People must engage themselves. All a leader can do is clear the way. Despite this, I often find overreaching conclusions from employee engagement surveys about leader’s capability that ought not be drawn, and decisions based on those conclusions that ought not be made.
Engagement is either in the nature of a person or it is not. Some employees will never be engaged no matter what you say or do because the business you want is not what they want. That’s fine, but perhaps they should be in a different role or in a different company. Other employees are simply disengaged from life, not just from your business specifically. You cannot fix that.