The issue with re staining is not that it was stained before. If it was just stained then you could easily re stain. The process for tinted finish is to completely seal the wood then the tinted finish is layed on top. Factories and furniture makers do this to save cost on materials and time on finishing. Thats why the chipped areas appear to be bare wood. The easiest way to fix this stand is to sand it down, reapply a sealer like vinyl sealer or even shellac then reapply a tinted top coat. Easy if you have it tore down and in a shop with spray equipment.
If you want to just repaint. Sand the bad areas real good and scuff the rest of the stand. Apply a coat or two of de waxed shellac your doing this so you dont have finish issues. Basically block the old finish so your paint doesn't fish eye. Your new painted finish can be spray paint if thats what you want to do. If your doing this in the house then obviously that's not a good idea. Your better off finding a waterbase poly acrylic wood finish and mixing it with 20% waterbased wood stain. Apply the mixture and you will have a new solid finish just as if you painted it without all the fumes in your house.
Eww, The alcohol trick only works for homeowner type finishes. Precat lacquers are not going to be affected by a little alcohol. NC lacquers will be dissolved but they havent been used commercially for decades.
Don