That little sticker (pictured) was sitting flush against the center bus on the trackpad chip. If a little drop of liquid gets in along the top of the trackpad, it can travel down the ribbon and to sticker. Add a little heat from the adjacent battery and its ink can be deposited onto the bus.
As I'm sure you've now guessed, this is what happened to me. It seemed to be causing an interference along the top of the trackpad [visible in the 'Show Live View' feature of Better Touch Tool (Freeware)].
I suspected a swollen battery, but mine was fine. The part of the battery that sits beneath the trackpad is encased in fairly thick plastic. I would be skeptical of anyone telling you its a swollen battery without you inspecting it. Removing the battery may just lower the temperature in that area, masking the symptoms.
I removed the whole ribbon cable from its ZIF connector and peeled off the stickers and took a cotton swab dampened with rubbing alcohol and swabbed the ink off the bus. The first few swabs were deep purple after swabbing. Its been over a week now, and my previously unusable computer has not had even a momentary relapse.
PRAM and SMC resets would only give me a few minutes of respite before a resurgence. And if you decide to pay to fix, you need only buy the ribbon cable and chip not the whole trackpad.
Temporary quick fix: disable trackpad in settings and use a USB mouse.
Attached: The underside of the trackpad with the user side of the computer up, trackpad ribbon cable removed