To whom should I apply for financial support for just a few months of Board membership?

As a (new) study association, you can submit an application to the assessor of the faculty with which the association is affiliated. The assessor is responsible for determining the number of  administrative months, following which Student and Educational Affairs (SEA) will send you a final allocation decision. A student association will receive from SEA an allocation decision which stipulates the number of months allocated. If you want to start a new student association, you should contact the Local Chamber of Associations (PKvV).