Nick; I have a 1939 Chevy Suburban Carryall and it has a one inch recess full width which was painted black.
On page 99 of"The First 75 Years of Transportation Products" published by Automobile Quarterly there is a picture of a 1941 GMC Suburban and it shows a plain bumper with no paint recess.
This book was given out to all GM employees in 1983. They show up at flea markets now and then.
Good Luck.
Stan Norrish