I found an old graduation film taken around March 1942, from the Hancock College of Aeronautics Primary Flight School. The "new" Army Service Forces patch (starting Mar 9, 42) along with the "outgoing" Air Force General Headquarters patch (ending Mar 19, 42) are both in the film. That should be able to narrow the date down to March + or - a month. One particular graduate has a Tech 4 patch along with what looks to be a bomb with wings. I read that some units used their own symbol for the "T".
Here's another patch from the film. Looks to be round with a circle, zero, or picture inside, and maybe yellow.
Here's the Hancock College of Aeronautics along with the Army Service Forces patch. G. Allan Hancock passing out the diplomas.
the example I was able to find was a Tech 4 with the AAF winged prop. This type rank patch was used for the air specialist for a short time before the war and was discontinued in 1942. The picture is a bit fuzzy and does look like a bomb with wings, but can't find an example of that.