Thanks undrentide, yes, I understand that "<noun1> が <adj>" modifies <noun2>, and I understand, in broad terms, how these modification clauses work, in this and other cases. What I am asking about here is the different types of relationships between "<noun1> が <adj>" and "<noun2>" that can be expressed in this way. What I tend to do in such cases is to just guess at any relationship that makes sense, without fully understanding what the potential meanings might be.
For example, I assume that 屋根が赤い家 means "house with a red roof" or "house which has a red roof". Here the basic relationship is "~ which has ~". However, 頭が痛い様子 presumably cannot mean "appearance/condition which has a painful head", which would be the analogous phrase in English.
My reply to Mike above was written in a rush, and I think it is not very clear. My understanding is/was that the whole of "<noun1> が <adj> <noun2>" functions grammatically as a noun phrase, just as "house with a red roof" does in English. Therefore I did not understand how 頭が痛い様子 can mean "appears to have a headache", as it seems to be the wrong part of speech.