Welcome back! The question is a good one, is it possible to define governance function in its most theoretical sense that can be used by any governing board. This is John Carver with Miriam Carver explaining the answer.
The most important issue for selection of board members is to first define what the board is to do, then determine the kind of person needed to do that job with a group. Most boards that are frustrating their staff because the are micromanaging were selected for their management skill. It does not see too surprising that they would therefore manage things.
These are sample characteristics that I recommend when looking for good board members:
Ability & discipline to think
Recruited for demonstrated commitment to the values and mission of the organization
Connections to the “moral ownership” and resources
Creative Thinker, Open Minded, Team Player
Time and energy to meet
Strong Ethics, Possess Integrity
You might think of some others…
Look for board members who will help the group produce the job outputs that your organization needs, the board’s contribution must include:
Linkage to “ownership”
Explicit governance values
Assurance of organizational performance
Additional tasks that the board may assign itself may include: Donor fundraising
You may think of others. . .
If you need the board to do these things, establish characteristics of people who have that capacity. If you are looking for legal help, you likely do not need another board member, you need to find pro bono legal help. If you have in Los Angeles County check with the nonprofit Public Counsel.
Increasing the board's size cannot ensure that the board will do more. Especially if the board has not articulated what it should produce as a group.
How the board elects and installs new members is in your bylaws. Look there first. If it does not serve the needs of the organization, revise them within the limits of the laws of you state or province.