The Sankt Goar line crosses the german town of Sankt Goar and separates the dialects that have t in words like wat and dat and the dialects that have s in the corresponding words was and das. Is this change abrupt? Does the consonant literally change from one side of the line to the other,does it happen gradually through slightly different pronunciations or do the dialects that are spoken near the line use both forms,slowly fading into just one of them the further away they are from the isogloss?
Isoglosses are generally drawn as these nice, hard-edged lines on a map. On one side of the Sankt Goar line, you have das, and on the other side, you have dat.
The problem is, nothing in linguistics is ever this clear-cut. Even the boundaries between languages are fuzzy: you can walk from Rome to Lisbon without ever crossing a hard line between two languages.
So isoglosses are a sort of "good enough" approximation. In general, someone on this side is more likely to use das, and someone on that side is more likely to use dat. But if you went to Sankt Goar itself, you wouldn't find half the people using das and half of them using dat: more likely, the people near the line use both versions, maybe interchangeably, maybe in a sort of diglossia (using das in some registers and dat in others). And as you get further away from the line, the probability that you'll hear one instead of the other increases.
Yes, this particular change is aprupt. There are no intermediate forms between wat and was (like *wats) nor dat and das. There may be places where you can find speakers who you either form, maybe separated by age. After all, at least in Saarland Rheinfänkisch (the dialect with was and das) is spreading into formerly Moselfränkisch (the dialect with wat and dat) territory.