Snap new pencil path to a middle node of another path

Is there a way to automatically connect/snap a new pencil-drawn path to a middle node of another existing line?

I’m drawing jigsaw puzzles that will be cut with a laser, and even the most minute gap where one line intersects another will cause issues. I would like to avoid a painful review of every line — zooming in; manually confirming the end of one line is snapped to a node of another; and manually adjusting that line to force a snap to another when necessary. There are hundreds of these intersect points.