A You do not specify what you have tried, but I suspect that it goes no further than persistent invitations and widespread sotto-voce mutterings, which is how most of us respond when we are too embarrassed to tackle things more directly.
First, it is important to get the head involved: you say she is a governor, which helps. All of us, however much confidence we acquire, are a bit in awe of the head. Use that awe.
I always tell heads they have a right to high expectations of us because we have voluntarily taken on an important job which affects them directly - and I suggest that those expectations should be made explicit. I advise them to adopt little tricks like jotting down the names of governors who say they will do something or come to an event, and follow it up. Writing is a powerful tool and makes it seem more of a commitment even if you throw away the bit of paper as soon as you are out of sight.
I also think it important to be explicit and organised about the various rules you make for yourselves - for example, everybody on two committees, everybody to take on a class attachment or duty month, everybody to choose an issue to present to the governing body, including initial research. These are just examples; you may favour other forms of agreed commitment. But whatever it is, spell it out formally and monitor it as a group.
You must also be more formal about apologies, ask for reasons and decide each time, as a group, whether you accept them. This is necessary anyway, if the six-month disqualification is to work. This is a dead letter if you are vague and indulgent about apologies, bearing in mind that the regulation refers to absence without permission.
If dates are fixed well ahead and not changed, you are on stronger ground to question apologies. Always notice absences or other derelictions and ask about the reasons.
If all else fails - and your colleagues are of one mind - you will have to talk with the offending governor on the basis that a governing body works well only if there is reasonable equivalence of contribution - his is unsatisfactory. You can do no more than make him feel uncomfortable but few are thick-skinned enough to stand that for long.
I have been taken to task sometimes for this severe approach, reminded that "we are all volunteers and can only do our best", but I honestly believe that the workload and the seriousness of the task are now such that it is not fair to the conscientious governors, or the head, to be content with low standards. I see "volunteering" as meaning more commitment than any other form of activity, not less.