[Brian in Tucson]

What year is your car? I'm in the midst of a complicated engine change on my 2001 base.* Neither of my PS pumps have an overflow hose, never heard of such a thing.
The only overflow hose I've seen on my car is the coolant reservoir overflow--which exits behind the right rear tire.

Before you started your work, did you notice any puddles?



*I'm putting an engine set up for manual transmission into a tiptronic car--requires switching wiring harness.