"I doubt that Gaelic was ever spoken in the Berwick region so if the signs around there are to be bilingual why not use Scots?"

Well Gaelic is of course spoken all over Scotland though speakers in the Borders tend to be few and far between and apart from learners are generally Highland incomers. Historically the area doesn't have much of a tradition of Gaelic 'possibly' limited to a few incoming Gaelic landowners in the early part of the last millenium. So you are right in that for the area the local dialect is a dialect of Scots and not Gaelic. Scots should have some recognition but at the entrance to the country you needn't exclude one to recognise the other.