I don't know if you've already come across it, but there is a section in the Color Classic FAQ that answers this question. Clicky.
1.1.5 — My screen is missing one colour. How can I fix it?
You most likely have a cold solder joint on the printed circuit board (PCB) that sits on the end of the neck of the CRT. In order to fix it, you'll need basic soldering skills and tools, so if you don't have these, find a friend who does.
Pop the back shield off of the board (it lifts right up) and inspect the board closely. If you see any solder points that are dull grey instead of silver, or are discoloured, or look physically cracked, re-solder them. To be completely thorough, you should remove the old solder, apply flux to the two areas to be joined, and apply new solder, but in most cases, you won't have to do that. In most cases, simply heating and re-melting the solder is sufficient.
If the above doesn't fix it, double-check all the connections in your wiring harness, paying particular attention to the video section. If one of those connections is intermittent or otherwise flaky, it can cause weird video issues. If nothing is wrong with the wiring harness, start checking for cold solder joints on the analogue board itself. If that doesn't yield results either, try another motherboard, or different VRAM. Bad VRAM chips or bad video circuitry on the motherboard have both been known to cause video problems as well.