Retreating to personality types, I would say that balancing task to relationships would start by using the Jung/Myers-Briggs test. Those who are introverted (finding people exhausting) would prefer the task-related styles more than the staff-oriented styles. The extroverted (who find people invigorating) would want and need people contact so would be more likely to be focused on staff. Of course, no one is all extrovert or introvert, so those who fall in the middle could embrace other styles. I cannot imagine what kind of individual would be happy in an opportunist style management position.
How is an individual’s personal interest in tasks and relationships related to how she or he shows task and relationship leadership?
The impact of management style can be reflected in a couple of examples. How that style would emerge can depend on a number of forces. It could depend on training – what was the philosophy of the teacher/mentor? Other influences would include the culture of the company. For instance, (I’m from Seattle, so know more about business there) the Boeing Corporation is an authority focused culture. The employees are unionized, because there is no other way for their needs to be considered, and strike every few years, costing them and the company significant economic and goodwill losses. (For an understanding of the cost of a strike, read Germinal by Émile Zola.) To protect this kind of management style, Boeing contracts have a clause that allows them to delay delivering a plane, based on uncontrollable issues: accident, (such as a fire) environmental (such as earthquake, inclement weather), and labor (strike) issues.
An organization that should be a country-club organization would be schools. The Seattle School district suffers from strikes, thus is either a paternal/maternal or authority complex. They struck this year, and have struck so many times I have lost track. That teachers are forced to strike for any reason to me is shocking, and shows how although the government on one side desires there to be quality education available to all, manages to get the workers, who have already made the decision they are accepting less pay and poorer working condition, so angry as to refuse to do their jobs. This kind of disconnect between people and management is toxic to our society. That government employees of any class should need a union is shocking. Government serves the people, so should serve its own workers.
Thus, if an individual needed to have a certain reputation within the community, they would need to consider how the company treats employees, and carefully select their job to match those requirements.
It is interesting that in order to figure out an aspect of leadership, one tends to retreat to another to assist in figuring out how to assess how a person would react.