'Mystery' Hose
Paul,
Some machines have that hose, and others just have a cap on the pump opening, so the hose is not a necessity. What it is good for, is to drain the water from the tank if the pump is clogged or stuck. Just bend the hose down into a pail, and gravity drains the tank. Makes repair work a lot cleaner and drier.
Blackstone also added a plastic cover to clamp on top of the motor, to keep water from dripping or pouring into the motor. Or you could just duct-tape stiff plastic to the inside of the cabinet, to make a roof over the motor.
The smaller, plugged-up opening in the pump was used for recirculating in newer Blackstones.
I have a few stainless tubs, which might be the same as what you have, if you feel the urge to change it out.
One other thing--I hope the hose from the tub to the pump is still flexible. It was hard enough stretching that hose when new. No wiggle room here. I always hated those things.