Adsto,
The actual colors used are, to a certain extent, whatever the Avionics vendor uses as his standard palette - there are two basic ones from SAE standards (Brand H & Brand C originally I beleive). But to answer your question about "minor" Cautions. Generally these will be covered by flight phase (e.g. Takeoff & Landing) inhibits in a modern EICAS. Otherwise they may be covered by system logic & electrical bus failure inhibits - in reality the system decides when & if the pilot will even know there's a problem for the majority of CAs messages at least compared to a simple idiot light.
How we did it when we put together the original CAS list on a Regional was to:
(a) ask the system specialist what drove his fault lights (often an eye-opener for them - a lot have never really thought about it)
(b) ask them what the pilot's action would be & how critical was it - this drives whether it's a Warning (immediate) Caution (knowledge but not immediate) etc.
and
(c) what might cause a false alert.
The latter is often the most difficult as it involves power supplies, redundant systems, specific failure cases etc. Another overall consideration is the type of aircraft - in general in RJs messages tend to get let through the filter more than Biz jets as its reckoned the crew are better at discriminating the severity of fault - but that's definitely a judgement call on behalf of both the team & the Project Pilot.