Your minutes should indicate which of the board members recused themselves from the board meeting. The wording would be something like this, “In accordance with policy Joe Blow left the meeting having declared a conflict of interest.” The minutes would then show the resolution being made, seconded, discussed and passed. Then the minutes would show that Joe Blow rejoined the meeting.
A person who is in conflict must leave the room. Staying in the room but being silent is not acceptable. Too much can be communicated with body language. Documenting the recusal is a best practice that helps to document and reinforce the importance of conflict of interest policies actually being followed.