Mrs.inConn is great at understanding Roberts Rule of Order. It's always good to have her weigh in on a bylaws issue. Many groups have a clause in their bylaws referring to Roberts Rules as the parliamentary authority for any issue the bylaws are silent on. My own group has this:
Section 4 - Governing Rules
The rules contained in the current edition issue of Robert's Rules of Order shall govern all issues of this organization not covered by these Bylaws.
Like Mrs. often advises - if your bylaws are silent, it's a good idea to refer to RONR.
Your bylaws should clearly define the Executive Board, voting members and non-voting members. If yours do not, you and your team may wish to revise them. Again, the bylaws should have an outlined review and revisions process.
As an aside, I've belonged to several types of groups. One didn't allow the president to vote, one allowed it only as a tie breaker and two allowed the office the same voting privileges as all other board members. What your group needs to decide is what works best for you.