Hello:
You are right, that the Declination of the object you are trying to image through the equatorial mount determines the about of drift to the north or south in your scope as you are tracking it.
It is hard for me to estimate what this would look like visually in my mind. But I suppose the star would look like an arc eventually and probably with a more gradual one than if you weren't tracking at all.
And if your mount is pointed to the east of celestial pole, the star will track to the north (if you have un-inverted opitcs and you live in the Northern Hemisphere it will appear

However, I forgot there for awhile you're in the South. But actually after I thought of it, it's the same there too.
And if you're mount is pointed to the west, the star will track to the south in un-inverted optics it will appear to go that direction too.
PS: I'm not real sure about those drift directions. But I do realize that it would drift one way for to the west or east of pole and is the opposite for the other.
In fact that's one way to align the equatorial mount is through drift.
Yeah someone should be able to figure it out mathematically. Like how much the drift is in mm is in an equation in a book called: The FX Exposure determination Method.
David