How Do I Add a Gradient to a 3D Shape?

When I use the pen tool to draw a shape and make a new shape layer, I can fill it with a solid color, a linear gradient, or a radial gradient

When I make that shape 3D, for some reason I can now only fill the shape using solid colors. Selecting gradient fill as an option, which adds a gradient to any 2D shape, simply makes my 3D shape gray for both linear and radial options.

Can you simply not add a gradient to 3D shapes? When I click the arrow next to "Add" right underneath my shape layer, I see an option for "fill" and "stroke," but the options for "gradient fill" and "gradient stroke" that are present for a 2D shape are missing. I would assume this means that I am unable to add a gradient to 3D objects, but then why is there still a full control panel for changing the parameters of the gradient as if I could?

Changing the parameters doesn't make any visible changes to the object. And the line with the two dots that you move around to place the gradient are on top of my shape, so it's not that either.