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If I host my own pictures and I swap out the picture but keep the url the same, will eBay refresh the Gallery Picture as well?
Even if you host your own pictures, a the Gallery picture is hosted on eBay, does not refreshed unless the picture for the item is updated either via the site or a ReviseItem call. If you want to change the Gallery picture, you will need to revise the item.
Changing Your Gallery Picture
API Documentation: ReviseItem