Thanks for all of the replies to this thread. My apologies for being rather quiet for a few months as I have been somewhat indisposed.
For those of you who I haven't already given this link to, I've done a trawl through various resources and come up with a bunch of Gaults from the Ballymoney area. It's a bit of a jigsaw, as most of the pieces – or families – don't fit together yet in lines of descendants. But someone may be able to shed some light. It's at www.gault.org.uk/history
Patricia, thanks for the info. Robert Gault – he of the shop in Ballymoney – is a relation. I think a first cousin once removed or a second cousin of my father. That would be descended from a brother of my gr grandfather. I do remember meeting him many years ago and recall that he had seen some family bible where at least one generation had been written Galt rather than Gault, so that's something to bear in mind when tracing back Gaults.
I'll take some time to digest the information you have given me. Many thanks.