Do the unused HDMI connector pins have dedicated conductors within HDMI cables?
On a normal Type A HDMI connector, all pins have an assigned usage. Except for pin 14, which depending on the HDMI version is Reserved (unused) or used for Ethernet or other odd uses. While an individual device may not use all 19 pins, a typical HDMI compliant cable should have at least 18 of those pins wired on both ends.

If you are trying to use an HDMI connector for your own purposes, that's up to you, but if you want it to work as HDMI AND your custom wiring at the same time,  it won't be possible.