Something about this is breaking my brain, but I'm not through my first coffee yet. Perhaps it's the "bidirectional" part of it.

Ethernet signals could be seen as bidirectional since two interconnected devices communicate and use the same cable to move data from A to B or from B to A without changing any wiring connections.

But a bidirectional HDMI signal? That would be, what? A signal going from a source to a display (the normal way) or from a display to a source (which would give us no results at all since displays don't output signals that can be displayed on a source).?

While the source and display of an HDMI connection talk to one another, and a handshake is actually two-way and thus bidirectional communication, I'm pretty sure that's not meant.

So let's do the famous "we see you have a solution to a problem and the solution seems like it might be impossible so tell us what you're trying to do and maybe we can come up with a working solution" move.

Let's back up and ask what you are trying to do. What are you trying to do?