You probably should look for some sort of HDMI breakout adapter that has test pin between 2 female HDMI ports or 1 male and 1 female HDMI port, then use your same fluke cable analyzer on them. You probably have to test the "pair" of wires together if they are twist pairs like the ethernet ones.Fluke can do what I need for network cables with their Fluke cable analyzer. Just looking for a similar tester for HDMI cables.
https://www.audioholics.com/audio-video-cables/hdmi-versions
In the end the cable testing may not be the right way to start, I would narrow down to whether it is the camera by swapping between 2 spots, then see if the problems follow the camera or the cable, then try a replacement cable. You are not troubleshooting an assembly line that will keep making thousands of cables with mistakes, it is probably better to replace a questionable cable if it is isolated to the cable.