Creating a 3D gold text effect

You're not doing anything wrong — the gray shadows and lack of shimmer are simply the limits of Illustrator's built-in 3D, especially the Classic effect. Your reference is a true 3D render (as RvdT pointed out, Blender), so Illustrator can only ever approximate it — that's exactly why Monika suggested a 3D app.

For the closest result inside Illustrator: use the newer panel, Effect > 3D and Materials (not Classic), set the material to Metal, and in the Render section switch the render mode to Ray Tracing. Ray tracing computes real reflections, which is what produces the gold shimmer and gets rid of the flat gray shading. It renders more slowly, but it's the big difference-maker.

That said, if the look has to match your reference exactly for the book title, hiring it out is the pragmatic answer to your original question — any freelance 3D artist can build this in Blender in well under an hour, which is less time than you've already spent fighting Illustrator's 3D engine.

This effect will be close to impossible to do in Illustrator.

What you would probably need to do is overlay objects to achieve this look. What will get very hard is the 3D front with the black letters.

I would suggest doing this in a 3D application. 

Still not able to apply a gradient after many hours of trying. I’m getting very frustrated!
I can apply a fill or a stroke to the text, but I cannot find a way to apply a gradient fill. I have created the gradient that you suggested but cannot add it to the text.

The appearance panel shows the fill as being the gradient but there is no way to add other fills or anything, and at the top it says Type: No Appearance. What am I missing? I also cannot save the gradient anywhere or add it to pre-defined swatches or recent colors.

This is absolutely a native Illustrator job — no AI needed, and you're right that it's about a 10-minute task once you know the right panel:

1. Set your subtitle in a bold font and fill it with a gold gradient.

2. With the text selected, go to Effect > 3D and Materials > 3D (Classic) > Extrude & Bevel (Classic). Add a bevel and some depth, keep the rotation at 0 (no tilt), and under Surface choose Plastic Shading — that gives the metallic gold shimmer. Play with the lighting to get the gleam you want.

3. For the black embossed front: duplicate the text, remove the 3D effect from the copy (via the Appearance panel), fill it solid black, and align it exactly over the front face of the 3D text. That creates the embossed black overlay.

Adobe's official guide to the 3D options:

https://helpx.adobe.com/illustrator/desktop/special-effects-styles/create-3d-graphics/create-3d-objects.html

If you'd rather hire it out, any freelance vector designer can knock this out quickly — but give it one shot yourself first!