Headless spirit is beyond a shadow of doubt still open to question (12)
I believe the answer is:
inconclusive
'headless' is the definition.
Both the answer and definition are adjectives. Perhaps there's a link between them I don't understand?
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for inconclusive that I've seen before include "not getting any results?" , "not settled" , "Not giving a clear result" , "Not leading to a firm result" .)