Well the trick is simple really, just donīt draw two lines from the exact same position
No seriously, if you look closely, you will notice that I do not actually start to draw the line from the exact position where the first line starts, since then the tool would only "pick up" the first line again. I always go a few pixels to the side.
You can see that very well at 5:20.
Another trick, if you absolutely have to draw the line from a marker point for example, is to drag out the original line a bit behind the mark (so that it goes through the mark), and then start the new line from the marker again.
I hope that helps