how can u tell if a relay stays open and pulls power from battery in a few days

Just find someone who knows what and how to perform a PARASYTIC BATTERY DRAIN TEST.

With key off, remove the suspect relay , gently start it back into place,, hear or feel it click?? If it clicks it is 'CLOSING' and sending voltage to it's designated circuit! Now, your best bet is to have a parasitic load test performed!!