Using a KX-6020 cassette deck with auto reverse to digitize cassettes for a non-profit. Bought this back in December, digitized about 20 tapes with no issue before this sound started.
On the "forward" setting, I'm hearing a mechanical "thunking" or "clicking". I do not hear this when I hit the play button for the other direction. Attached is a picture of the gears that are making the noise.
Here are two videos: https://imgur.com/a/JGX3P5I
The first video shows the gears and sound while playing a tape. The second shows what it looks and sounds like when I manually turn the gears.
The repair manual for this deck identifies these gears as "reel gear assembly" (white gear) and "FF gear assembly" (black gear). I'm a bit out of my depth here but would like to try to address this myself before I go to a professional, if possible.
It does play back just fine, but I am worried about the cause of this and what will happen down the road. These are tapes that are not replaceable. Thanks for your input!

The smaller belt does not look right. You should replace it with a belt made specifically for the model. It could be contributing to your problems.
The belt is the same on both mechanisms, and sees to match what the SM shows. I would think if it was the belt it would manifest the same problem in both play directions, which it doesn’t.
Kenwood did not use round or grey belts. You or whoever can down vote my comment, but I’ve serviced dozens, and that is not the right belt.
I'm just confused on how a belt can cause a gear slipping problem, and in one direction but not another, and why it was a problem that only recently manifested. Additionally, that round belt does not turn the gears which are making the sound at issue.