This is Damon's answer:
Guardian Pillar does not become an exhausted character. The location support card exhausts to allow Guardian Pillar to commit to a story as a character.
The Silver Key prevents readied characters from committing to a story.
While Guardian Pillar has not been exhausted it is not a character and therefore does not fall under The Silver Key's passive effect at all. It is only by exhausting it does it count as a character.
In short, no, you may not commit Guardian Pillar as an action.
As a passive its ability lets you exhaust it to commit to a story as a character. The only time you can commit characters to a story is during the commit step of the framework action (as of right now). As a passive its effect alters the rule about what can be committed. If it had a trigger, like Action or Response, or even Disrupt you could do it at any point that an action of that type could be triggered.
Committing a character is a framework action, that is to say, it is something the game creates a step for and has specific rules governing. The only way for a player to commit a character is through these framework actions. Now a card can become committed to a story through a card effect, but that is not the same thing. For example, playing a card means paying its cost and placing it on the field from your hand, putting a card into play means using a card effect to put the card into play from any out of play area. The end result,, a new character being in play, is the same, but how it is achieved is different.
The same is true for committing a character and a character being committed. The Black Dog is put into play committed, it does not go through the commitment process which is what its response effect triggers off. A Black Dog can never respond to a Black Dog.
Now if there were ever a card that said "Action: Pay 1 to put this character into play. Then, exhaust and commit it to a story of your choice." The wording on that card would specifically create an additional commitment process where a Black Dog would be able to trigger its effect.
Does that make sense?
So, Zephyr was right all the time:
GP has to be committed during its controller commitment turn, and the Black Dog cannot respond to a Black Dog as it skips the commitment process
Thanks for your answers!