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If the bench is solid, I just set it on the bench to pin. If not, I have a plate of steel that I can use.
If you wish to use your vise, the same unit comes with a shaft if you search for "drill...

I have had good luck using a cheap drill chuck from Harbor Freight.
1-2-half-inch-jacobs-keyed-chuck-45731.

Other places have them but higher cost.
Good on Ya!
~Richard