Saw this Ebay sale that included "Palm Olive" Gillette razor These were Ball Ends, each with original box. It's the first I'd heard of this model. I'm curious if this promotional tie-in razor had a Palm Olive phrase embossed under the base plate such as the Ivory Soap razors did.
There were a few versions of the Colgate-Palmolive Gillette promotions. Two I have seen are the red outlined boxes and the ones in that auction with green borders with silver-plated Old Types ... I've also seen a NEW so I'm guessing this collaboration was late 1920s, early 1930s.
Palmolive as one word may lead you to a better search.
These are the 'Good Will' razors, a promotional offering. A number of different Gillette models were used in these offerings; buy Palmolive shave soap, get a Good Will razor for free. ca '31-'34 or so.