Couple of things Brian.
Are you wiping things like the tailstock quill over with oil now and again ? Is there an oiling point and do you use it? If there isn't an oiling point it would probably be best to remove the quill now and again and put a bit of oil on it and the thread in the end of it. Same goes for however the handle is held in place but a bit of grease would be best there between parts that rotate against each other including bores and shouldn't need doing very often.
Your best bet for oil where you are is probably grade 32 hydraulic oil. It needs to be a mineral oil and these are. I can't see any on ebay oz, only stuff for cars etc. The type needed is the sort used in JCB's and fork lift trucks and things like that. You may need to buy 5l
so it will last a long time. It's reasonable stuff to use on the lathes slides as well so if you are going to have a lathe it's worth having around which ever one it is.
Then the tailstock itself – I only just looked before more rabbiting

If I had one like this jam up the first thing I would look at is the axial parts from 408 to 413. The end of the handle might be too hard on the 408 bush. The thread in the handle and the nut form a lock nut famous for loosening over time so when you use the handle it screws down hard on the the bush. The same thing can happen on slides made this way. A better option is a keyway. The bush might move under load. 1/2 drills are BIG for this machine. The talstcok quill is only used as a support for a die stock to square it up not to force it on and each time the chip is broken the tailstock has to be moved back from where it was.
Pinch bolts are a bit of a pain. They are only intended to pinch things not clamp them up rock solid. When drilling they should be slackened right off. It's the fit and the length of the bore outside of the pinch area that looks after the alignment. I suspect this area might be your problem looking at the end of the quill in the photo or / lack of oil and or condensation – it looks a touch corroded. I can't see how 404 could get over tightened – that should have a round thread free part on the end which is a nice fit in the slot in the quill. Wouldn't surprise me if all Baby and similar lathes didn't have.
If the pinch bolt needs to be used because the spindle fit in the bore is so so a lot of care is needed. The quill still needs to be able to slide through it fairy easily and the screw feed provides a lot of mechanical advantage. Sound like the fit was pretty good.
If 408 jammed when you were getting it out you probably knocked it out of square. That would cause it to mess up the bush and the area it sits in. If you want to do that sort of thing easily it's best to find something with a square end near the diameter of the bore so it can't knock it out of square.
If they are not hardened the ends of quill can expand out a bit due to the morse fitting. They can anyway if the tapers are slightly out. Either way- something to watch out for – getting slightly stiffer when the quill is fully drawn in. It's less likely to happen on substantial quills. Many lathes have rather low diameter quills.
John
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