Weird tearing/artifacts on the AG-1980
 

Can anyone tell me what is happening in this video?

https://www.youtube.com/watch?v=7C8tuNbeTAM

The first half is with the AG-1980. The second half is with a cheap Sanyo.

You'll notice that with the Sanyo, the tearing isn't visible. I cleaned the Panasonic and saw no improvement. I then wondered about tracking, but then realized that the tearing effect, very reminiscent of physical damage to a tape, only reared its ugly head when static visuals were displayed on screen. High contrast images (such as bounding boxes or white text with a black border as seen in the sample video) seems to trigger it the most, especially when horizontal lines are being displayed. In sections of the tape where the imagery is more natural, such as footage of the outdoors or people in a room, the tearing disappears. This leads me to believe that it isn't an issue with the tape being read, but how the smarter features of the player are interpreting what it's seeing.

I did wonder if the higher contrast just made the tearing easier to see, but after staring at 20 minutes of video, I'm convinced that isn't the case. My Panasonic somehow just doesn't seem to like "graphics" being displayed on screen.

Adjusting the sharpness and toggling the TBC had no effect.

These VCR's are over 3 decades old, Components are aging and out of spec anything can throw them out of balance like an old man, To revive these beasts a full restoration is the only way, Replacing bad components, recalibrating to factory specs, at least electronically but ideally both mechanically and electronically.

From the video, it looks to me like the AG-1980's TBC was turned off, because with it on, bare minimum I would expect to see the horizontal wiggling stop.

I agree. No lineTBC correction seems to be present.

But is it baked in?

The OP had already said he toggeled the TBC on and off and has not effect.
The content is not baked in based on the two samples from different VCR's he linked above.

Well, sort of, after poking around some more. I want back to make a comparison video to show the results with the TBC running, and noticed some really weird skipping that I didn't have before. Turned it off, and it went away. Turned it back on with pressure on the switch, and roughly 95% of the errors disappeared. Loose connection.

What type of switch Panasonic uses? The JVC uses a digital pulse to turn on and off the VCR via a tactile type push button on the front panel.

It's just a simple mechanical sliding switch. I've got a tiny piece of plastic wedged in it now to ensure it behaves.

You can also spray some Deoxit if it has an easy access to the switch cavities, it will clean the contacts.