Update: In addition to the TV/FM System software there's a Power Mac 6500 specific update you may need to get everything working. It's called the 6500 Video Input Update. Here's a link to the download:
http://download.info.apple.com/AppleSupport_Area/Apple_Software_Updates/English-North_American/Macintosh/System/CPU_ Specific_Updates/5500-6500/5500-6500_Video_InputUpdt.img.bin. It may help even if you're not running Mac OS 8.1 or earlier like the Readme states.
As proof of that some Performa 6400 owners running Mac OS 9.1 claim they still benefit from the 6360-64XX-54XX Update. That update was originally designed for Mac OS 7.5.X. Not Mac OS 9.1. It amazes me at Apple's ignorance of these important updates.
Just because they were released before Mac OS 8.6 or Mac OS 9.1 doesn't mean those OSes won't benefit from the updates if installed on the correct model of Macintosh. I also suspect that despite its confusing model specific name the 6500 Video Input Update may also help 6400 owners struggling to get the TV/Video System and/or TV/FM System to work with Mac OS 9.1. Both Macs use IBM PowerPC 603ev processors.
The only difference between the two Macs is the speed the processors run at. The 6500 also has a bit better onboard graphics card. The only weird thing is the 6500 doesn't have 8 MB of RAM soldered to its logic board. Only the 6400 does. The 6400 has a 40 MHz bus. The 6500 has a 50 MHz bus. That's why Sonnet's G3 uprade runs at 400 MHz in a 6400 & at 500 MHz in a 6500.
Maybe my first reply wasn't clear enough. Here's a link to a page that has detailed info on the TV/FM System Mac OS 9.1 issues:
http://www.zone6400.com/files/AppleTV-Videosystem.html. One of the links is a download for the TV/FM System 1.5 software itself. The link is to a web page on the 6400 Zone. If it works I would recommend you e-mail the author of the site a thank you. He's looking for feedback of other users of software like that.