I did not explicitly schedule meetings for the sake of meeting. I looked for opportunities to come my way when I was invited to be a part of a discussion or presentation and focussed on nailing down those 5-10 minutes. I always prepared a question or two on strategy or vision to ask if provided an opportunity.
This could also be different because earlier in my career I worked for very large organizations. I could imagine having a more close relationship with your c-suite at a smaller company.
Early on, I worked in growth stage start-ups and typically worked closely with the c-suite team. My main feedback would be as PMs we see ourselves as product and technology experts. What I learnt is when you can tie that to customer and market problems, your interactions become even more powerful with the c-suite. This leads to opportunities like creating a new product line, solving a company OKRs because they see your skills as a company leader beyond a product lead.
Perhaps the best way to answer this is in terms of what NOT to do
1. Do not waffle, digress, rat-hole, debate, over explain, use technical or other jargon, assume they know or care about details or nuances
2. Do not be overly serious or conversely too friendly, casual, obsequious, flatter, play the devil's advocate, try to nail them with hard questions, or ask them open-ended questions that require a whole other conversation
Even beyond C-suite, a PM should tailor his/her message to the audience. A typical mistake aspiring leaders do whilst communicating with the leadership is get too much into nitty gritties and details, whereas an CXO, by virtue of his position, needs the information and his action points as succinctly as possible.
Breaking away from this trap is key to being an effective communicator
Carrying forward on the question above, it is imperative for you, as the mediator, to make the stakeholders seek common ground. Practically, this could involve a common session with. both of them exxplaining the pros and cons of their polar opinions. As always, it is you 3 against the problem and not one against another. Can't stress this enough,Being a manager neccesitates being an empatethic individual
As you grow in the org this moves from your typical 1:1 structure to a more nuanced, influencing style which cannot be demarcated as such in an answer.. Suffice to say being a problem solver at hand, on a day to day basis is what being an PM is-> if one can manage that, everything else flows organically
Managing a team can be , simultaneously, the most rewarding and most frustrating aspect of your career, hence choose wisely
For most, managing people becomes a forced transition in search for personal growth-> this is very dangerous, coz if you can't manage people (and people are idiosynchratic) than you and your reportees end up having a bad experience