1. They show positivity, even when things are not good. People who are successful are positive. No matter what happens, they stay positive and calm. They do not show their stress and disappointment. They also do not welcome those who are not positive. When a complainer comes to them, they support them by helping suggest a solution, not by listening to their complaints. Remember: success attracts success. The opposite is also true.
2. They show respect and appreciation for others. They respect others, if they disagree with them. They won't storm out of the meeting even if they disagree with the decision. They won't give you orders but will make suggestions. They appreciate their colleagues and always give credit to others when they deserve. They welcome success of others as their own. Transparency is another side of their respect to others. They share information freely and without fear.
3. They are assertive and know how to say "no". This does not mean that they are "yes" people. They have their understanding of what they can or cannot do and share it with others. However, whenever they say "no", they do it with respect and explain the reasons. Most often, however, instead of saying "no" they will suggest an alternative. E,g, they would say "I cannot meet with you this week to provide an overview of this topic, but here's the list of links that cover it", or delegate this, or share their advice in a different form. They are committed to supporting others, and their colleagues know it.
4. They build relationships. Even if they do not have a specific reason to reach out, they always do. They want to learn how the enterprise functions, they want to meet people in different departments and discover how to collaborate with them. They don't miss a company picnic or a townhall - not because they want to show their support but most importantly because they care, and it shows. These relationships will help them resolve many situations in the future.
5. They maintain integrity. In order to have others respect them and them you as a true leader, people with emotional intelligence respect basic values: they support their peers, share information with their teams, celebrate successes, their own and ones of their peers, and contribute to team work. They are value-driven, not governed by their own ideas and priorities. They do not lie or backstab, instead, they take ownership and pride in the job that they do while being collaborative and innovative every day. They exuberate energy and their feeling of excitement is contagious.
There are many more qualities of emotionally intelligence people, but the five above are most important to me. If you are an accomplished professional and are concerned that you are not getting promoted as fast as you expect, use this list as your checklist in making sure that you show high emotional intelligence in your day-to-day job, and you will succeed.