Well 8/4/4 would imply red has 16x the resolution of either of the other two. Each bit per gun doubles the range of values it has.
I suggest you try the trick using a vertical gradient on a 256 pixel tall screen if possible - a horizontal gradient will always have some bleed in it. Turn off dithering also. If you have a genuine 8-bit gun colour, a 256 tall gradient will have a unique colour every line giving a smooth gradient. If you have 4-bit, it will be approximately 16 bands you will see.
If you see that green has 64 bands and that red and blue each have 32 it suggest an RGB 565 arrangement which is far more sensible (its your basic 16-bit RGB format).
This gives you 32x64z32 = 65536 colours and is not too bad. A well dithered RGB 565 display is almost as good as your HAM8 (since green is the brightest colour, it makes sense to give it the greater resolution so that the steps are smaller).
If you see red as completely smooth, green and blue as 16 bands, it implies the rather insane RGB 844 format. This format could only have been chosen by some tired HW designer who had no knowledge of colour theory at all. First of all, the green channel should have the greater bit depth (where the total resolution is not divisible by three) and no single R/G/B channel really needs more than 2x the resolution of the others. This is why RGB 565 works so well, but RGB 844 is just bobbins ;-)
