I have a very strange question...(don't you love it when posts start this way?)
Using single line search - search members of HH where both A1/A2 have same last name - no blue & yellow HH icon
Search patron where they are A1 of HH - you get the blue & yellow HH icon
Search patron where they are A2 of HH - no blue & yellow icon
My question is, why does the blue & yellow icon only appear for the second scenario. In all instances I have Include Individuals/Households/Organizations all checked.
The blue and yellow icon only appears when the household record itself is returned by your search query. So, I think the question you really want to look into is when you have "Include household" ONLY checked, how is your single line search parsed, and then why does it or does it not return the household record?
It could be that the household has an alias name for the A1 individual. Otherwise, the household is treated as only having a last name.