Hi Meriwether
I'm no expert but i do get around and about a few of the lanes here in the Borders from time to time.
As previously mentioned Mungo's Walls is indeed a farm, although it's nearer to Duns than Edrom. It's very close to Wedderburn Castle, basically sharing a boundary with the castle grounds, and maybe a mile or so from the town of Duns itself. There is a photograph of the West entrance to the castle on wikipedia, Duns is left of the gates, Mungo's to the right.
http://en.wikipedia.org/wiki/Wedderburn_CastleMany of the farms in the Borders still have the old cottages standing, whether that applies in this case i can't be sure but it wouldn't be a suprise to find something remaining from the period.
Still no idea why the name came about but it's around four miles to the English border and not far from Swinton so could still tie in with the old religious route from Coldingham to the Border Abbeys.