MacBook trackpad occasionally behaves erratically

So I've had my 2015 Macbook Pro for about 7 years now. The trackpad has been (occasionally) behaving erratically for the last 2 years or so. Out of nowhere the cursor would quickly move up and down on its own performing random clicks and multitouch gestures. I'm convinced it's a hardware fault because I've had this happen even on my bootcamp installation as well as the boot select screen.

What's interesting is that I experience such behavior once every few months. The issue persists for many hours, even upon restarting, resetting SMC (not sure that has any effect) and eventually returns back to normal, only to reappear a few months later.

I found an app called FingerMgmt that displays all inputs received from the trackpad and it was interesting to see my trackpad registering false inputs from the right side and made a screen recording for reference.

What could be the cause of this and how could I fix it? I haven't spilled anything of my Macbook and the only time I opened it up was to replace the SSD.

EDIT: As requested, here's an overview of my battery condition

As @danj suggested, I decided to go ahead and replace the battery on my MacBook Pro, and while I was at it, I also removed the trackpad to inspect it. It was full of dust, some hair and other nasty stuff that had settled there over the years. I cleaned it off as best I could before reinstalling it to the computer. I suspect this accumulation of dirt is the culprit and I'll confirm in a few months if the issue doesn't reappear.