Apple TV 4K Random HDMI signal flick flacks and loss

It is recommended to use HDMI 2.0 (18 Gbps, Premium High Speed) cables for 4K HDR.

Using cables rated for lesser bandwidth might hit its limits, depending on settings, and causing HDMI errors.

Do the issues go away when using lesser settings (SDR, 1080p, 4:2:0, 24 Hz)? If so, then it seems likely that the issue is in these settings and the bandwidth that they require.

Borrowing a recommended cable for a few minutes could confirm that such would solve the issue, before removing in-wall cabling.

From that behaviour it sounds like your using an older generation of HDMI cable from would have been ideal for running the ATV2. times have changed and newer formats demand a higher bandwidth. Do you have a newer device at home that uses a HDMI 2 cable? you could try that and see if it solves your problem... failing that officeworks has a cheap 2m cable for less than $5 you could just plug that into one of the HDMI side ports and see if you still get the flickering. if it performs well then buy a longer one.. the 5m cables are $8. just tape the end of the new cable to the old and pull it through the plastic pipe.

Reduce the Bandwith, change Refresh rate to 30Hz, not optimal for TV content or games but should work fine for movies