Hello Aeroscout, and welcome.
I'm afraid I know very little about Naval aviation, but is that ranking from the Royal Navy Fleet Air Arm? If it is what I think, Airman Mechanic, then this was a rank, I think roughly equivalent to Sergeant, and was given to aircrew who I believe would be trained as Observer/Gunner, or Wireless Operator/Gunner, on such types as the Swordfish, Barracuda, Avenger etc.
Certainly FAA Avengers were very active in the Pacific campaigns, and there are probably people here who know much more than I could possibly know! If it happens to be an American rank, then there's even more chance!
If your father was in the Royal Navy, then I would think your first avenue would be The National Archives (formerly the Public Records Office) at Kew, London, where the relevant Military Records listings will be held. From there, given you obtain the info regarding Service Number, Unit, dates etc, it will be possible that the FAA Museum at Yeovilton can help with operational details, if they have them. Both of these organisations have on-line services, although you would need to check with them as to what can be obtained without a personal visit.
Sorry I can't offer more assistance, but good luck with your search.