Chosen Solution
So my Playstation 4 has had a few instances now where the Playstations video feed will cut, and not work for some time. Initially was just before purchase, but it has seen more aggressive failures in the past few months. The first failure 2 months ago prompted me to do a resoldering on the port itself, in the event of a failed connection, and that got the input working again for some time, perhaps two days of frequent usage. About 2 days ago, the output once again stopped, and this time I had a full replacement port at the ready. An hour of work and the usage of my hot air station later, I managed to resolder the port, and inserted the new, replacement port. This worked well enough for about twenty seconds, where the PS4 reported it was recovering data (I pulled the plug instead of a proper shutdown, silly me.) before the feed cut abruptly (not unlike an HDMI cord being yanked out) and cut to the black it was facing before. Experimenting with the HDMI cord and televisions, we know both instances are working, meaning the issue is localized in the PS4. So if not a fresh install on the HDMI port, what are other avenues to explore as fixes?
Note that the HDMI Encoder chip commonly goes bad from hot plugging the HDMI cable when the PS4 is switched on. What happens is that when the HDMI cable is plugged in or unplugged while the PS4 is switched on this can sometimes creature a small power surge which is just enough to kill the HDMI chip over time. As these consoles are not grounded properly (3-prong connection into the PS4) they are suspeticale to this problem. So make sure to only unplug or plug in the HDMI cable when the console is switched off and the power cable unplugged.
I had a similar issue before with my PC HDMI output, and after an hour of test & research, I found that I put the HDMI cable near a power cable which creates an alternate magnetic field that messes with the HDMI signals, so I separate them and everything works fine.