Silly to be lacking a brain (5-6)

I believe the answer is:
empty-headed
'silly' is the definition.
(thesaurus)
'be lacking a brain' is the wordplay.
I cannot really see how this works, but
'be' could be 'head' (heading is a kind of being) and 'head' is found in the answer.
This explanation may well be incorrect...
'to' acts as a link.
Can you help me to learn more?
(Other definitions for empty-headed that I've seen before include "Vacuous" , "Frivolous" , "Unintelligent, stupid" , "Given to frivolity" , "Scatterbrained" .)
