The shape suggests that it might be used for pre-stretching the tire so it goes on easier (and the slowly settles in the groove as it contracts. But you still have to take the truck apart to get the wheelset out for the TT removal and install. I don't know what the piece of brass rod is for.
I seem to recall similar tool (included with a package of universal traction tires) being sold decades ago. I think it was made by Stewart.
EDIT: Yup - I found it. It was made by Virnex and sold under STEWART name. Looks identical to the Calumet one - Calumet is probably new incarnation of the company. Here is a fuzzy photo showing the tool and the clear tires.
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