Eiren make an Arcana check 

Not trained in Arcana, but here is Intelligence: 7

Which glyph key are you using?

You have two keys one for the Forest of Recovery and one for Iron Golem Foundries.

Wisdom Save: 15

Corvin peers at the map for a bit, getting his bearings.  Eventually he looks up and says, "Looks like we're just beyond the white gate.  Pretty much right in the center of the doomvault by this map."

I am trying to open a portal back to the iron golem foundries, so think that has to be the glyph key from there, yes?

(The room is still in the Golem Laboratories)

Eiren tries to activate the black gate but fails.

here is what Corvin sees on the map...

So skulls 2,3, and 6 all lead into (and out of?) this room. The entrances from both 2 and 3 have White Gates in the hallways, while skull 6 leads directly to a new room.

Quote from VanderLegion >>

(The room is still in the Golem Laboratories)

 (But the glyph key is linked to the black gate in the iron golem foundries, right?)

Quote from Flyingmatthew >>

Eiren tries to activate the black gate but fails.

(So like, I touched the key to the black gate and nothing happened? No fizzling energy or anything? If so...)

Eiren will take a moment and try to see through Qu'oth's eyes, to see if everything is still as they left it moments ago in the previous room.

(Correct, nothing at all happened)

Eiren concentrates for a few minutes on Qu'oth. Looking through Qu'oth's eyes he sees the room you just left. Besides the White Gate being closed again nothing else seems to have changed. 

(Does Eiren know of a way to attune a glyph key to any black gate? Without already having a glyph key that is attuned to the zone that the black gate is in?)

Eiren shrugs and looks around. “So it looks like we’re not getting out this way. I can try and have Qu’oth do something for us up there, but I’m not sure what.”

"What happens if we try and exit through one of this mouths?" Eiren asks, pointing to the northwest one. 

Does anyone what to try it?

Eiren will go for it.

Xavier will go to examine the skull doorway Eiren wants to go through.  Are there any hidden levers or buttons or compartments or something 

perception 3

Corvin nods at Eiren's suggestion and does what he can to help if needed (help action for advantage on ability check of one is needed and it would make sensed for me to be able to help)

Before Eiren tries to leave through the skull mouth, Xavier looks to see if there any buttons or levels that might help. He doesn't find anything like that, but he does find a skeleton resting in the corner of the right side of the skull and the room's wall. Looking closer at the skeleton he sees that there is a Mace resting a few inches away and writing scratched into the wall.

 Eiren tries to leave the room by climbing into the mouth of the northwestern skull (number 6) and out to the room beyond. However as he steps into the skull’s mouth, macabre laughter erupts from the northwest corner.  Eiren is teleported to the 3 5 skull across the room (number 2) and comes tumbling back into the room, falling prone and taking 1 bludgeoning damage. Make a DC 15 Con save or take a -1 penalty to Condition checks and saving throws. 

(There was an intelligence saving throw for Velmine way back then that I missed so here it is.)

Intelligence Save: 16

Velmine is following Xavier on the methodical examination of the room instead of trial and error, and she tries to see if she can read what's written. (Knows only Common, Infernal, and Thieves' Cant.)

Here's the Mastiff's Wisdom save for following his master through the gray mist 18