As I'm writing the first draft of my WIP, I kept tripping up on when to use the colon, semi-colon, dash etc. So I asked the trusty members of my writers group (every writer should be a part of one), we lovingly call The San Gabriel Valley Inklings. Here's their response . . .
The semicolon should be used quite sparingly. (Strunk and White, or some famous style manual, says something like "When you see a semicolon, kill it.") It is used when the text on both sides are complete sentences and closely related. E.g. "I'm not going to work today; my hair is a complete mess." Many editors would advise using a complete stop (period ) between the two complete sentences whenever possible, rather than a semicolon. (In addition, the semicolon is useful for what we used to call in high school English "the mess-of-commas rule." This is when you have a list of items that would grammatically be separated by commas but the items themselves contain commas. A good example is a list of cities with their states. In such a case, use semicolons between the items to distinguish each item in the list. E.g. "Our travels took us to Denver, Colorado; Lincoln, Nebraska; Chicago, Illinois; and Toledo, Ohio.")
The colon doesn't necessarily require a complete sentence following it, but what follows should specifically explain or restate or specify what has come before. If what follows is a complete sentence too, I capitalize the first letter after the colon; if not, I don't. (See how I slipped a semicolon in there?) E.g. "Suddenly he knew the truth: All his friends were gone." In your example, the colon is appropriate, with a lower-case "a" following it: "It will be a good scar, young Watcher: a sign of healing." Alternatively, when what follows is not a complete sentence, there might be times when you could use a long (em) dash instead of a colon to heighten the drama. E.g. "There it was--the gold he had been searching for."