It is always tough to sort out when everything shifts fine except a single cog, especially since it has been shifting poorly in that 2nd position cog for 4 years.

If it were the first position, I’d be inclined to think you need to lube the cable because gummed cables don’t un-gum going to the 1st position cog as the rear derailleur return spring has less tension. It doesn’t hurt to pull the cable, clean the housing and install a new cable.

I’ve had a bad or poorly spaced cog in the past and for me it was more a matter of trying to figure out if that one cog spacing was off. If you have automotive feeler gauges you can check the cog spacing. Maybe re-visit the high limit screw.

It is frustrating and sometimes it is just going through each component to determine the culprit. If there was nothing glaring, and the hanger is fine, I’d start with checking chain stretch and replace it, if it didn’t fix it maybe even a new cassette.

John