Bump Offset is omitting areas.

[mAlkAv!An]

First of all you'll need to apply some blur to that height map, sharp transitions like in your texture will always cause issues.
That being said a simple parallax effect is pretty limited and won't allow for a large height ratios anyway. You can however chain up multiple BumpOffset nodes to get some nice results whilst still keeping the material fairly simple.

[Dunfisch]

This one only had sharp transitions (and a normal map which was just ghastly) due to being forced to make do with GIMP, which isn't really up to par in terms of efficiency. But the gist is that I can presumably achieve a much better result if I can get a smoother heightmap? I'll give that a spin.

[Dunfisch]

I'm trying to put in a rather simple bump offset, but for some reason I have a peculiar issue... behind which I suspect lies some mundane
reason I didn't pinpoint yet.

As can be seen in the attached images, it does push out the parallax just fine - but only for the actual bricks. The grout is simply left out entirely,
as though stenciled away by some alpha channel mask. I don't see where I have set up anything of the sort though, which is why I'm so mystified. It's not like the grout is full black either.

Now I know a full parallax can entail many more nodes, but I'm not looking for that, it doesn't need to bend perfectly around edges.

The greyscale images I was using for the heightmap suck, because I hadn't gotten around to install Photoshop yet, so I contended with GIMP. I don't
see how that would do make any difference though, it's still a good old image as normal as they come. Gradation could be better, obviously, but still.

I can post the files I used in the material, if necessary. Tomorrow I'm plugging in Photoshop too, see if a cleaner heightmap image somehow solves it.
Doubt that though.