The most important thing I learned when I first got into managing people was the importance of trust. It cuts across all types but it is especially important for 6s to have trusting relationships with others. I don't know about other 6s but I don't judge people negatively because they lack consistency. These things being said, I may not be typical in that regard and I do believe for many people consistency is quite important. For 6s, what may be most important is personal loyalty to the individual vs. some kind of predictable behavior. Is there something you might be doing that causes them to worry about their personal security?
I'm not sure what will work for you but here is what worked for me. After learning that trust was important, the single most important thing I learned was to extend that trust towards others. When you trust others, they trust you. The second thing I did was to try and understand and appreciate the differences between people. I would in a sense become a student of the person - to seek to understand them, their motivations, what they are like, what they enjoy doing and be able to understand how and why they would react or do things that they did, and why different people were coming into conflict with each other. Typology was a tool that supported this but it was just a tool because two people of a similar type can be vastly different. The third thing I did was to truly care about them as individuals. I would become personally invested in supporting their growth and their career. If you care about people, you are loyal to them and support them in their careers, they tend to trust you. As a 6, if I were to have a boss like that, it would engender a lot of trust. However, I will be the first to say that there have been some, particularly those with performance issues, that have been well... an issue. Performance in my experience though has little to do with type. Finally, the #1 thing I have consistently heard over the years that people want and don't get enough of on the job is appreciation. Specific verbal appreciation is probably the easiest thing to provide. This feeds into the 6s need to be secure.
With respect to being the "weapon that people pull out when they need it", I think I have run into this issue to some degree because I can move pretty aggressively into action in crisis situations. Earlier in my career, I would do this "white knight in shining armor" thing and just take over in problem situations. I was very effective with it in achieving short term results. However, it probably wasn't the best way to inspire and build the morale of those I was leading. As time went on, I developed a style in which I didn't come up with all the answers. I would instead facilitate others coming up with them.
Not sure if that helps but those are some thoughts.