The very phrase "employee engagement" is nothing without the employee. We are all employees, and at times it's easier to blame the employer for our woes without taking a look in the mirror. I've worked with many employees who thought the grass was greener elsewhere.
Let me start by making a fundamental point about behavior at work. People's attitudes are caused by how they perform, and they determine their performance. In short, they are both a cause and a consequence of behavior.
Simply setting goals for individuals can make a major impact on their motivation. If individuals accept the goals and see the behavior as worthwhile, they will be highly motivated to pursue these goals.