I THINK you are just in time. There will come a point when governors must set feelings aside and do what the future of the school requires, in close co-operation with the education authority. But I think you might just be able to avert serious trouble. When problems start to focus on important school meetings - a common symptom - it's only a matter of time before it's noticed, and staff will be approaching you. Then it will spread to bigger meetings with parents and outsiders, and it becomes difficult to turn back.
I'm often talking down the role of the chair because traditionally it's been more overdone than otherwise, but yours is a situation where an informal friendly approach is the best possible first step in the rescue operation. It doesn't need to be over-dramatised, nd certainly not judgmental, but the head should be in no doubt that he is in grave danger and that this is probably the last chance to avert it.
If either you or the chair is available to spend a little time with him just before meetings - with just one drink perhaps - it might help him to relax while he talks through the difficult issues. I think that twilight time between school and an evening meeting is dangerous.
You might also be able to discuss the workload with him, discover what he finds stressful, and see whether the way the governors organise the work, and perhaps even the way some governors behave, could be changed. There may be problems within the school which he finds hard to share but leave him in no doubt about your support.
Befriending and keeping company may not seem very big contributions, but they will make a difference. It is a lonely job sometimes and just knowing that his problem is shared may be a relief to your head.
The education authority will almost certainly be very understanding and gentle with him if and when it's their turn to lay it on the line, but the trouble is that by that time the problem may be common knowledge and then it's too late.