I have found info about this unit....the 405th was a B-25 Mitchell squadron for all of WWII. They were supplied with their first A-26 Invaders in January 1946. They flew from the following bases in WWII:
First overseas base--Breddan, Australia, August 1942...they had B-25Cs and -Ds, the first B-25s to be stationed overseas.
Some forward-staging took place, but next "permanent" base seems to have been Durand Airfield, near Port Moresby. They moved there in November 1942 and stayed there for about 15 months. Next move was in March 1944, to Nazdab Airfield New Guinea, and they stayed there until 1 October, 1944. During this time, they traded in their -C and -D model B-25s for new -J models. Nest stop was Pitoe Airfield, in Indonesia, where they stayed until late January 1945--at that time they moved to Lingayan Airfield, on Luzon. Half of the 38th BG's bombers and aircrew were sent forward to Puerta Princesa Airfield, Palawan, in June 1945 and attached to the 42nd BG, 13th AF. These planes and crews were later returned to Lingayan within a few weeks. I did not find info on the breakdown of the planes sent, so it is possible that 405th planes and crews were part of the mix. In mid-July the 38th made preparations to move to Yontan Airfield, Okinawa. This was the last base the 38th flew from during WWII.
The 405th was actually changed to a non-flying unit in 1946, and then reverted back to BS designation in 1947, supplied with B-26C Invaders and TB-25 Mitchells. The entire 38th BW was inactivated in 1949, and reactivated in January 1953, with the 405th having the same dates and events. In April 1955, they traded in the Invaders for B-57 Canberras.