Photoshop: gradient down the length of a path (Stroke Path)

Question

In Photoshop CS6, I want a B&W gradient along a path, with a uniform width, the gradient always perpendicular to the curve. I drew a path, used Stroke Path, with a brush that's a very tall line. I got close. Two issues: 1) the gradient decreases in size (?) but Shape Dynamics is off, 2) the gradient is always vertical (see pic). I want the gradient (the vertical brush) to be perpendicular to the path.

Answer 1

Fairly easy with a gradient applied to a path in Photoshop CC, not sure if this is possible in CS6. I can't recall. CS6 is getting fairly long in the tooth and it's difficult to give support after 5+ years of deprecation.