I currently find the ends of my freestyle lines to be a flat shape when I want a triangle like shape: 
I want the lines to vary in thickness when arriving at a "dead-end", and to fade out to a single point, instead of two that create the flat square shape.
Where can I adjust the end-line thickness of a freestlye line?
This is in Blender v2.79b.
I've managed to come up with a decent result using the 2D Length and Angle settings.
I first used an Along Stroke modifier (thanks Robin Betts) for the line thickness in the Render Layer Properties -> Freestyle Line Style:
This by itself didn't do much, so messing with some other settings, I managed to get the Min 2D Angle and the 2D Length values to get me a close enough result to the one I 'm aiming for:
This may not be the best way, but for me, it works fairly well. This is what I now have:
This way does give you different stroke widths on the mesh, giving it a more hand-drawn look which I was hoping to achieve in the first place.
EDIT: I reposted the first pic, which was originally:
This gave the mesh occasional bumps in the lines drawn, but in case anyone wants the curves for the rendered picture above, this is what it used.
..And another way, texturing strokes. (Here, in Blender Render).
This texture, at 1024x1024, is going to be used to multiply the alpha value of the stroke. It is white where the stroke is to be opaque, and Black where the stroke is to be transparent.
The left half of the illustration shows the texture.
The right half shows how it splits up when 'Use Tips' is checked. The blue region is repeated down the stroke, the red region constitutes the tail, and the green region constitutes the head.
In the 'Texture' tab, check 'Use Textures'. In this case, because the main stroke texture is continuous, the 'Spacing Along Stroke' setting is only visible as the length of the taper.
When you hit the button to 'Go to Linestyle Textures Properties', you will be able to adjust
Other than the panels shown here, the settings are at their defaults.. (Image Mapping, not shown here, must be set to 'Repeat')
With some tweaks, (In this case I set a minimum stroke length in the 'Strokes' tab of the Line Style settings to get rid of short strokes).. this is the sort of result..
You can see some segmentation of the stroke due to the repeat spacing.. if you rescaled the bits in the original texture, you would be able to maintain the taper length while bringing the spacing down.
