Type I photos generally get a significant premium over Type III, though the market on any photos is highly variable, so working of a single datapoint (such as one old sale) would be difficult.
RMY has one type III of your photo that sold in 2020 for $450. It's one datapoint, but RMY has a few photos with Mantle and Day, and the close-up one (like you have) is clearly the nicest. Other, less appealing photos with Mantle and Day (and others) which were Type I photos went for less, so I do believe it was the draw of the image. Those sales were also in 2020 and the photo market is more expensive today than it was then.
My guess is that in auction it goes for at least $1000, though as others have noted, it is hard to predict photo values.
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