Wrench question - can't get 2nd gear

I’ve played with the adjust screw on the rear derailler for quite a while and although I can get all gears when moving from 10th to 1st, I cannot get 2nd gear on the way back up. It jumps straight from 1st to 3rd unless I turn the adjuster so far that I can’t get 1st at all.
There’s about 1500 miles on cassette and chain. The chain is well within it’s wear limits and is cleaned thoroughly each week.
Any ideas ?

When was the last time you changed your derailleur housing?

Check the henway
.

And, you should be using the H/L adjust screw to line up the derailleur with your cassette H/L. Then use the barrell adjusters.

Dirty derailleur - dry cable guide at the bottom bracket - shift lever indexing gear sticky / spring issues . Campy or shim ?

What’s a “henway”? About 4 pounds …

Are you referring to the 2nd largest rear cog? A bend derailleur hanger can do this. Perfect shifting in the lower 7 gears, then jumpy up top as the slight chain angle now with the jockeys not aligned because of the bent hanger.