It is in the style of middle Georgia, though one also finds it in some places in south Georgia as well, and occasionally in the north. It is usually on the thin side. You are correct that it is a vinegar-tomato sauce and does include mustard. Some cooks use ground dry mustard, activating it with water first, of course, and others use prepared mustard. Lemon is often included.
As a starting point try:
2 T unsalted butter
1 T veg oil
2 cloves garlic
1.5 c ketchup
1 c cider vinegar
.25 c Worcestershire sauce (optional; if not using, replace with vinegar)
.25 c prepared mustard
.5-1 t cayenne
.5 c brown sugar
the juice of 1 lemon
Heat the butter with the oil over med-low heat till the butter melts. Peel and crush the garlic cloves and add to the pot. Raise the heat to medium and cook til the garlic is quite fragrant, stirring often, and just beginning to brown a bit. Remove the garlic cloves from the pot and discard them.
Whisk the ketchup into the butter-oil mix then whisk in the vinegar and Worcestershire. Whisk in the mustard and cayenne next then bring just to a simmer. Stir in the brown sugar and lemon juice and stir, allowing the sugar to completely dissolve. Heat a few minutes more, adjust salt; done.
You can certainly add or delete ingredients and/or change proportions to taste.
