When defeating a boss that is required to unlock a Pantheon, the Godtuner appears on screen beneath the health bar and blinks.
There are 5 notches in the Godtuner section of the Inventory. Each notch corresponds to each Pantheon in Godhome. Each notch changes appearance according to the completion status of the corresponding Pantheon (which includes the Bindings used).
The circle in the very centre of the Godtuner, when viewed in the Inventory, glows when there has been a new boss added into the Hall of Gods. When all the new bosses have been checked in the hall, the light turns off.