I chuckled reading these last two responses, not because they are wrong necessarily, but because I know myself better than those authors. Believe it or not, the suggested "hammer" fix, or some derivation of it, did occur to me. I can, with high confidence, tell you that it would not have worked. I would likely have had a deformed aluminum tube that simply wobbled even more. Further, I would likely have broken the pin which is not brass but rather, "pot metal". I believe this because it bends too easily, something I saw when I reinserted it into the brass fitting. In fact, I am happy that I went and purchased a correctly sized punch rather than used a nail, which is what I would have done. At least that is what occurred to me.
If you are into photography, search on "copy stand" - these can be very high priced. That little table top stand was low priced and came with a light table that used a cold-cathode fluorescent lamp. It eventually dimmed and I did find a replacement bulb but it was about $35 and I ended up buying a much nicer table brand new. Granted, the new one has the typical digital PWM dimming which is fine for tracing a pattern but basically useless in photography.I still have that old light table and may use LEDs with it if I can ever figure out to dim it without PWM.
I replaced the copy stand with this one:

Look at that bad boy - rock solid - not cheaply made - not elegant, but it does what it is supposed to do quite well and has worked for years. An $bay purchase and the seller was the manufacturer. It was something like $45 and I admire that design. I have searched on DIY copy stands and I have yet to see one that I felt that I could build as cheaply that is as solid and works as well.
That left the old table-top with the option of tossing or fixing. It will now get some limited duty.
For me, this one was a clear win, thanks to the help I received..