Hmm sounds like possibly you could have a bad pickup? I've had some guitars have great sounding positions, and just one bad one. Usually it was always down to just the pickup itself. I have to ask how old is your Tele? Vintage or new? Also do you happen to know if your pickup pole pieces are Alnico or Ceramic? This can also help to know what could be going on.
If your pickups are Alnico, they could be losing their magnetism and you're experiencing issues in your tone when you're on just the neck pup. I had one guitar I remember, a strat, with the same kind of issues you're talking about. I tried the capo trick too and that wasn't the issue at all. It was an old strat 70s, the pickups had been swapped out before form the previous owner. He said the neck and middle pups were off a 60s issue strat and Alnico, and the bridge was a newer ceramic generic pup he pulled out of a different Japan copy strat.
The bridge has the best loudest tone on it being ceramic pole pieces. The neck and middle on the alnico pole piece pups sounded like crud. I found I'd have to turn my volume up which only made it sound even worse and broken up in spaces. And mind you the pup heights were set at a reasonable low height so the strings weren't being pulled down by the pickups. The simple fact was that those old 60s alnico pickups, had lost their strength.
I got a neck and middle pickup out of a MIM Fender strat I had laying around, the middle pup was also reverse wound so that was a nice upgrade for this strat. The problem however was completely solved! No more Stratitis! The new neck and middle pickup also being Ceramic, had the best tone and I or whoever else owns it later, will never have to worry about those old alnico pickups losing their magnetism. They really should of switched over to just ceramic pole pieces but people love the sound of old dying pickups.
If you can't find a solution on your own, if you can get a hold of a new pickup for neck, try installing it and see if your issue is gone. It might just be a weak pickup on its last leg. Even the newer guitars that are built with Alnico pole pieces will go bad over time quick. Especially those who lay their guitars against their amps lol Those magnets on those speakers are killing your Alnico pole pieces in a matter of time. I know some dudes who leave their guitars like that cause they think it looks cool like they're always ready to play. But they're always complaining their guitars just don't sound right anymore lol
Good luck with it, hope you can solve the issue and get it back to playing.