Pretty broad and simplistic to ascertain the possibility of answers as well as taking in account numerous differences. Perhaps you should look at redifing the question to get the answers you seek.
What I mean is leadership is more than influence and more than just rank. A newer or more junior FF can have more leadership skills and influence than the company officer. The styles depend on the person. You can have the book smart vs the experienced, you can have the lazy to the overzealous. Influence up the chain can depend on how rpomotions are done, seniority vs testing, written test scores over years of experience and so forth. Leadership can also be viewed in a different perspective, are we talking about managing a scene or managing a house, crew, dept, etc. Is leadership synonomous with managing (I would disagree) one can be a good manager but a poor leader.
Please explain to me how your influence has changed as you promote up the chain.
You leave a gap here. Such an assessment can point to leadership just about promotion vs the perspective of a junior FF to that of a senior FF or their perspective on those holding rank.
FEMA has an independent study on that very subject. I haven't had a chance to read it not like my chief who say's he did it in 8 hours. Maybe you should check it out! It's 240.a
I did a radio show on how to deal with negativity in the fire service with a great friend of mine, Chief DeAngelis and we spoke about individual personalities and how some officer's lead from their own. This in part can be "bad" if they have habits and qualities for which are not positive. We are all born with the tools needed to be a good person, "influence" as you put it comes in many forms, most personal belief and character traits were instilled during our childhood upbringing. There is a saying you are a reflection of the people you choose to hang out with, (when you were younger) so choose them wisely. In our older lives, negativity definatley loves company. Good fire officers cease the negative behavior / habits, while weaker or less educated officers just laugh at the behavior to be part of the group, or even turn a blind eye...