How do you handle two lines drawn on top of one another?

The first line sets a bunch of pixels in the stencil buffer that somehow then need to get unset before drawing the next line, no?

I'm actually really interested in this as I'm having a really complicated time doing what should be relatively simple 2D CAD-type stuff with any of the modern graphics APIs (Vulkan or DirectX 12). Any time I want to draw a world-coordinate vertex thing with a device pixel width dimension life just gets horrible.