Q. Should “cotton gin maker” have a hyphen? Does “cotton gin” here serve as an adjective, necessitating the hyphen? I’ve consulted CMOS and am still not quite sure. Thanks!
A. Good question! According to the hyphenation guide at CMOS 7.89 (see section 2, under “noun + noun, single function”), when a phrase like “cotton gin,” in which one noun (“cotton”) modifies another noun (“gin”), is used to modify a third noun (“cotton gin” modifies “maker”), the phrase would normally be hyphenated: cotton-gin maker.
That said, some editors would omit the hyphen. Not only is “cotton gin” entered as an unhyphenated noun in Merriam-Webster (with no adjective form, hyphenated or not, listed with it), but unless the surrounding context isn’t obviously relevant to cotton gins as opposed to some kind of process for making gin with cotton (whatever that would be), there isn’t much chance of confusion without the hyphen.
In sum, add the hyphen to be on the safe side, knowing that you can instead leave it out if that’s your strong preference (provided you’re consistent). In other words, this is a gray area (like the spelling of gray).