The BASSA branch is much bigger, so I imagine he was full time too, until the dispute started. Would or could the branch secretary become an implied full time position and therefore custom and practice, so requiring flying duties, just to stay in check. That is how I see any potential appeal, but I am sure we would all have heard about it, if this was the case.
I think this may all be academic as I think it will be a cold day in hell before BA re-employ DH - even if he were to win an appeal all he will gain is a little money. As soon as the elections within BASSA occur, he becomes an irrelevance. So in historic terms DH is a busted flush, it is a certainty that this dispute will end and when that happens it is all over for DH unless UNITE decide they want him on their payroll, which I personally doubt.