Agree with above, the only other thing I will say is some old shifters get gunked up or dry, and they can do all kinds of funky things. Over the years, especially when MUCH younger, I never seemed to be able to get a worn or unhappy shifter to get happy again. Likely things get a little twisted over time, etc.
However, I do think that if when you pull 4th it goes to 2nd, I would be looking inside the shifter, not linkage unless the linkage somehow is loading the arms left to right.