You can do a gradient map in Photoshop, too. It's a layer effect. But what I think you actually want is to use the height data as a bump map for shaded relief, yes? Similar to this (only better, of course):
You may need a better heightmap, since this one will give you terracing. The idea with a heightmap is you want to have a smooth gradient from peaks to valleys, not a contour-line look. The heightmap's values correspond to elevation at a given point, so if you have an image where there is a sharp transition from one brightness to the next, that represents a sheer cliff—one pixel at, for instance, 300 feet while the adjacent pixel is 100 feet in elevation, with no slope between them.
That said, the way to achieve a look similar to the one I posted is to use the Lighting Effects filter.
Import your heightmap in as a layer on top of everything. Ctrl-A to Select All, then Ctrl-C to copy. Now turn that layer off and store it in the bottom of your layer stack in case you want to come back to it later.
Switch to the Channels palette, create a new channel, and Ctrl-V to paste the heightmap into your channels list. Turn it off and turn the RGB channels back on. You don't need to see it, you just need in the information to be available to the filter.
Switch back to the layers palette. Now, assuming you've been working in layers, go ahead and copy everything you've already done by selecting all the layers and dragging them to the New Layer icon at the bottom of the palette. This will duplicate all of your current layers. Merge them (Ctrl-E) to get a flattened copy of your map. If all you have is a flattened image already, you can skip this step, of course.
Now, with the flattened image selected, go to Filters > Render > Lighting Effects.
The Lighting Effects filter is rather complex, so I'll walk you through its controls while I give you some recommended settings for your desired look:
First, I don't know how many or which of the presets in my Photoshop are custom, so I'm going to start with the Default Style. If you happen to have one that says "Neutral Directional," though, that's a great place to start.
Light Type determines what kind of lighting is being simulated. For a shaded relief map, we want to simulate the Sun, which is a directional light (the Sun is technically a point light, but it's so much bigger than the Earth that the rays come in effectively parallel). The line that appears in the little preview window indicates the light angle. The square at one end is the source and the circle is the target. Shaded relief maps are conventionally lit from the upper left, so place the circle in the center and the square in the upper left corner (I did it backward in my example, which probably makes the map appear inside out since it's lit from the south). If you move the square toward the circle, the apparent light source will be higher. Depending on the aspect ratio of the image, the arrangement I indicted gives a vertical angle of between 30-45 degrees. You'll notice that the preview image brightens up as the dots move closer to one another because the surface is reflecting more of the light to the imaginary camera. You can compensate for the overall brightness with other settings, though, so don't worry about that for now.
Obviously you want to leave the check box "On" or there won't be any light on the map.
Intensity controls the brightness of your Sun. This is the first control that can counteract whatever happened to the brightness when you were moving the light's direction. Move this slider back and forth until the brightness of the map roughly matches the original image, then move it to the left to make the map about 25% darker. This will prevent the lit sides of your mountains from blowing out to pure white. But don't go below zero, or the highlights and shadows will become reversed, which looks really strange.
Focus should be grayed out because a directional light doesn't use it. If you were using a spotlight, it would control the rate of falloff from the center of the light to its edge.
Gloss is a matter of taste. Moving the slider toward shiny will emphasize the highlights, possibly causing them to blow out. Moving it toward matte will reduce the contrast, possibly making the map look dull. I tend to err on the side of matte since I can always improve the contrast with more traditional Photoshop tools like Curves and Levels.
Material is another matter of taste. The difference between plastic and metal (in the shading sense, at any rate) is that metals reflect their own color. So as you move the slider toward metallic, the highlights become more tinted by the underlying color. As you move toward plastic, the highlights get whiter. Essentially it's a saturation control for the highlights. Personally, I like about 50% metallic for shaded relief.
Exposure controls the overall brightness of your image. This is the control you'll want to use to do any final corrections to the brightness. However, you can replicate a lot of its function using Levels on the finished product, so don't get too finicky with it, since you don't have reasonable feedback from that tiny preview.
Ambience will allow you to control the black levels. If your shadows are too dark, raise the ambience. If the entire image is washed out, lower ambience.
Finally, there's the Texture Channel, and this is the most important control in the interface (and as such should really be at the top). From the drop-down box, select your heightmap channel. If you didn't rename it when you made it, it's probably called Alpha 1. This loads in the bump map information and lets the filter do its thing. You'll immediately see the relief appear in the preview image, though it's still too small to see anything really useful there.
Leave White is High checked, since your heightmap has the mountain peaks as the brightest spots.
Height determines, as expected, the apparent height of your mountains. Turning it all the way up will create very rugged-looking terrain, and may make the map appear large in scale (small in extents). For a regional-scaled map, that's great. For a continental map, move it more toward flat, which will smooth it somewhat and make it look smaller in scale (large in extents). More mountainous does bring out smaller details, though. Again, it's a matter of taste.
Since I've worked through this tutorial, I might as well upload the results of my little tutorial, since they're considerably better than that earlier pic:
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