I recently bought a Jacobs chuck and a Morse Taper for my lathe. I think
I'm missing a step somewhere. When I mount it in the tailstock, it just
spins freely, leading to a less aggressive drilling action than I hoped
for.

I can make it drill by holding it still with one hand, but that doesn't
strike me as particularly safe, and it's certainly not comfortable.

What part of this am I missing?

BobMac