First of all, there is no point ringing anyone on this issue to expedite the matter. The people you reach won't have any details other than what you can find out from the baggage tracing website. The online tracing system is the only source of information, and will be updated as soon as someone finds the bag, wherever that bag is. Ringing someone to enquire about a lost bag will, at best, just get them to look up that system with your file reference - something that you can do yourself.
Ringing the Heathrow Ground Handlers won't help - you have established that that is one place it definitely is not - so there is nothing they can do, or tell you, until the bag is found, somewhere, and its details are entered into the baggage tracing system to initiate the process of re-uniting it with its owner.
Most bags DO show up, but it can take a few days. Just be patient and wait for new/additional information to be loaded into the system.
You did say, however, that the bag was YOURS but that you were not travelling. Did your father, by any chance, tell anyone at any point in his journey that he was carrying a bag that was not his? Or was there anything in that bag that may have raised suspicions during a scan or search?