The 31st was a National Guard division primarily from Alabama, Georgia and Florida. However, it was not purely limited to those sources and it is very possible the 106th originated out of Kentucky.
I wouldn't worry about "Michigan" as that is where he died, there was a lot of intervening time between 1917/18 and 1941.
There is evidently somewhere a 106th Engineers Association who erected this plaque somewhere in Vicksburg.

You might try these addresses for more information (these are publicly listed on the Internet):
106th Engineer Combat Battalion (WWII)
Mr. |Earl R. Stonefield
8513 Pennsylvania Run Road
Fern Creek, KY 40228-2539
(502) 239-3020
Co A, 106th Engineers
Mrs. Bob Weisinger
120 N. Sunset Terrace
Jackson, MS 39212
(601) 372-1384
L-