I think it's desperately in need of repotting. Either your soil is too soggy, or there's too much salts (fertiliser) build up in it. Looks like it's Epipremnum aureum (pothos). They will send out runners towards the dark, an 'instinctive' response when looking for a tree to climb. What's the rest of the plant look like?

Thanks for the interesting runner info.

> What's the rest of the plant look like?
Had to move a lot of other plants out of the way to take a picture of (part of) it.

It was started from an unidentified two leaf section "rescued" from a staircase, then kept in water for more than a year before hitting potting mix. Never expected it to grow like Morticia Addams' favorite plant "Cleopatra" after that kind of start.

After 3 yrs, I'd change the soil. What's visible in the new pic looks pretty good! Scraggly pieces can be cut off and re-rescued, stuck back in the pot. The little brown nubs sticking out of the stem near each leaf are root nodes. They turn into actual roots if they hit water or soil. When doing that by either method, remove any leaves that would be in the water or under the soil.

Thanks for the comments and suggestions, appreciated.

I agree, the rest of your plant looks good, especially compared to that offshoot in the first pic.

Update for those interested. The "weird" offshoot in question is up to about 1 ft long and apparently has decided to now produce a nice looking leaf. The other main vines continue to grow, 'though probably more slowly now that the windowsill micro-environment is cooler due to lower outside temperatures. (Will certainly re-pot after the winter.)
Thanks again for you observations.

Definitely interesting. TY for the update. Good vibes to your plant this winter!