Hi Dwayne, welcome to the forum. We`ll sure try to help you solve your research puzzle. It may take awhile so stick with us, you have a lot of good clues and there will tons of sources & records to check.
A couple of things i would suggest is go to a local Library & search newspapers of the time frame, newspapers usualy had some mention of the local boys in WWII.
Another is to contact the local VA Hospital, they may have a copy of his records.
I dont have much time to do a lot of research at the moment, but i found a few things that will help.
The 434th AAF Base Unit was located in Santa Rosa, California, & i think Hamilton Field was close to there.
I wondered why a 23 yr old would be sent back to the States in Dec of `44 unless he was a casualty, but in a Nov `44 report of the 818th EAB there appears to have been a normal rotation back to the States of men that had served in Iceland.
The 21st Engineers was a full regiment in `41, The Reg went from the US direct to the Invasion of North Africa in Nov `42 & serve in NoAf, & Italy for the war.
2 Companies of this Regiment did go to Iceland in `41
I find nothing on a 21st Eng Const BN (separate).
Now for Iceland:
On & July `41, 2 Companies of the 21st Eng Aviation Regiment landed at Rykjavik, Iceland with the first group of Task Force 4 of the 33 Pursuit Squadron.
These 2 Companies were soon redesignated as the 824th EAB.
The second group of Task Force 4 landed 16 Sept `41 and include 2 Battalions of the 5th Eng Combat Regiment.
The 7th Eng Combat Battalion, organic to the 5th Infantry Div. landed in May `42.
Any part of the above units could have landed in Jan when your granddad did.
for now, here is a website for the IX Engineer Command that has a tremendous amount of information on Eng Aviation units including monthly operation reports & histories: