Most non-profit boards pay $0. The Internet Society is one of them, with Barnes taking $0 from the organization (as board members, they also have to disclose if a related organization pays them):

https://projects.propublica.org/nonprofits/display_990/54165...

There are a few exceptions to the boards-get-paid-$0, but they're rare and doubt personal financial motivations are part of the decision.