No taper mate here, I make sure that the MT stays clean, first off I do not spray any finishes on the lathe if I ever use any at all.
Every time I am going to use a MT in either the spindle or tailstock, I first blow through the MT, next the MT gets a dowel with a rag stuck into it and rotated, often the late is flicked on/off and the mandrel gets wiped with my hand before inserting with the flick of the wrist.
Alluminium Tapers I would never buy or use, knowing how alluminium grabs other metals and gets scored, it is the wrong material for this and many other uses.
And yes the oiled cork with a cap on it sits in my metal lathes tailstock, as I don’t use the inboard very often and the tailstock on it even less, so keeping it clean and rust free is a must.
On the small lathe the tailstock is as often off of the lathe as on, the thing is prevention is the way to go, so I keep the MT and ways etc clean.
In a drill press the mt used has a tang to prevent it from rotating and is used with pressure to keep it seated, on a lathe it is different, with say a jacobs chuck in the spindle and no tailstock pressure to keep it seated, a drawbar needs to be used.