>Technique for pulling new cat6 through wall using old cat6 cable?
It's really just going to depend on what things look like behind the walls.
For relatively clean/straight runs I've just tied the old cable to the new cable and pulled it through. But if there's a lot of tight spaces in the run, or sharp turns, or staples, or whatever... Those knots can get stuck and hung-up and not work.
For narrower runs I've tied or taped a pull cord to the old cable... Pulled the cord through... Then tied/taped it to the new cable and pulled that through. Also - if you use decent pull cord it'll be rot-resistant and you can leave it in-place to deal with future pulls.
Sometimes, though, you'll find runs that just cannot be pulled/replaced like that. Sometimes the installer will staple things down and that cable just isn't going anywhere. Then you're just looking at having to run a new line from scratch.
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If so, I will order it! But now that it's so thin, what would be a good way to connect to the telephone wire? Is it still a tape, or something else? Maybe a knot.. or.. why not both
This is made for the job, and it's cheap enough: https://www.amazon.com/gp/product/B0026TA6WK
I have also used this wire-pulling lubricant for helping with getting stiffer shielded Cat-6 cable through conduit.
As has been said, you want something like this:
https://www.harborfreight.com/3-8-eighth-inch-x-48-inch-flex-drill-bit-94317.html
I've used it extensively.
You're going to need to learn to patch drywall, and with the flexible bit you can cut your access hole/slot about 2' down and snake it in. I've thought about making a 3D guide that will self center the top plate so I can make a very small hole but... I'm good at patching and it's faster.
You'll cut the access above wherever you put the drop. You do NOT want to go sideways unless you're accomplished or running power at the same time (aka, cut a 2' high section of drywall all around the room to run new outlets).
In the attic you're going to have to find where you 'poked through'. You can use this:
https://www.harborfreight.com/100-ft-fish-tape-3891.html
But that' is usually used for electrical, and is a PITA to get into tiny holes, but does bends well.
I'd recommend getting this instead
I've got both and I find myself using the fiberglass 'poles' to probe insulation positions in the attic.
You've got to be smart and pick where the wires come in- you don't want an outside wall because there may just not be the height to get to where it pops out. So inside walls if you can.
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Get a length of nylon or pull rope
https://www.amazon.com/Breaking-Strength-Klein-Tools-56108/dp/B0026TA6WK
And put that in with every wire you put in. Trust me. That way you can pull something else if you need to.
Leave about 1' of wire in the access hole for recuts. Wire is cheap. Labor is expensive.
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Good luck.
A string, Basil! Always leave a pull string in the conduit.
https://www.amazon.com/Breaking-Strength-Klein-Tools-56108/dp/B0026TA6WK