As I recall, not all fan belts were of the 'red'/'brown' color. Some were black. Like most all of the components that went into the Ford Model A, Henry had several different suppliers. Some were red (my 'Red' belt says 'Gates'), others were black. I also have 'Gates' belts that are black. A look at the MAFCA / MARC Restoration Standards* should provide a 'sense of direction' in this regard.
* MAFCA / MARC Restoration Guidelines: section 3, page 3:
"The original fan belt was either black or reddish brown."
Another alternative to a 'reddish brown' belt, is this Black belt from Bratton's: Part #12790 - "Original wraped style belt made from the FORD blueprint by Dayco for Bratton's"