The original board was selected as an outgrowth of that original study in 1985, the Strauss-Laird study. At the time, Paul Kirk and Frank Fahrenkopf were the chairs of the Democratic and Republican national committees respectively. They took steps to incorporate the commission and served as the founding chairs. They ended their partisan political service shortly thereafter, and there has never been any other tie between a board member and the political parties.
There is a nominating function that is outlined in the bylaws, which is internal to the board. There's a nominating committee, which is named by the chairs and consults inside and outside in looking for new members of the board.