Pounding with mallet? Pickle forks? Yikes!!
If the tapered piece, whatever it is, won't eject when you back the tailstock ram all the way in, then the best solution is to run the ram out all the way and pull it out of the tailstock. Take a piece of brass or aluminum rod an stick it down the threaded hole from the back of the ram and tap it with a hammer and the taper will get ejected.
I've found this to be a fairly common problem with #2 morse taper products I've purchased recently. They don't seem to sit down into the taper as far as some of the older, original South Bend tooling.
For a permanent solution, you could ream the tapered hole in the tailstock ram a little larger but I really do not recommend this. A rather crude but very effective short-term solution would be to just drop a small slug of brass, maybe 1/2" diameter by 3/8" long down into the tapered hole in the ram and just let it live in there. It will effectively lengthen the tailstock screw and make sure the taper gets ejected when you back the ram into the tailstock.
Some folks drill and tap the end of the tapered appliance and put a small machine screw into it, giving it a little bit of extra length.
The deluxe solution is to make a new tailstock screw that's about 1/4" longer than the original and thus fix the problem permanently.