Image on left is from 4 days ago, but the pimple was slowly forming over around 2 weeks.
The goop was sticky, not oily. Earphones are Panasonic RP-TCM130.
I was not able to find an explanation.
Something to increase cable lifespan, lubrication, rubber disintegrating, sweat and earwax that somehow got into the cable, dielectric grease, no clear answer.
At first I thought the wires just somehow twisted. Nope.
Have you verified the specs on OPs headphones?
Maybe I missed it but I don’t see where OP said this happened while connected to a phone.
They’re earbuds. You’re going to using them with a phone, maybe a laptop, or even in a pinch maybe a desktop. None of those output enough power to melt through a rubber cable without severely destroying themselves and never working again. OP would be posting “my phone exploded and I’m deaf now” not about the cable having a pimple.
Even my dedicated amp, a Shiit Magni outputs 6 watts with both channels combined, and ain’t nobody connecting shitty earbuds to an amp. The rest of the cable is going to sink away the heat from 6 watts before the rubber could get hot enough to melt.