Video flickers on and off randomly, physical HDMI connection is fine

I bought a used Xbox, it is modded (I didn't know of this), it's a 360 Slim Trinity. The HDMI output flickers on and off, more so on than off, and it often happens (weirdly) as I move through menu screens.

I've tried different HDMI cables and they seem to behave a little different? One of them straight up just makes the TV say unsupported video.

I've tried the same cables and TV on another Xbox 360 Slim I have from a friend and it works just fine.

Wiggling the cable doesn't do it, which probably means it's not a physical connection issue.

Going to pick up a component cable at some point to see if the issue is just HDMI related.

Any ideas? I'm already ready to hear that the hana chip needs to be replaced.