Effect of soulless gaze:
"When you demoralize a creatures more than once using Intimidate, you can create stronger fear conditions rather than increasing the duration of the shaken condition."
I know that fear effects are cumulative, stacking to a maximum condition of panicked, and that panicked creatures cower if they cannot flee. source
I also know that fear caused by the intimidate skill does not stack with itself (or other fear sources) without soulless gaze. source
MY QUESTION IS:
If soulless gaze is used on a panicked creature, does the creature cower like with disheartening display? Normally fear stacking caps at panicked, but cowering is a fear condition that is stronger than panicked, so does soulless gaze consider cowering to be a "stronger fear condition?"
Fairly certain I found the answer. The intimidate skill description on d20pfsrd uses the specific wording "create stronger fear conditions" and from the context, this is understood to mean moving from shaken to frightened/panicked, or from frightened to panicked, as with normal fear stacking. Soulless gaze uses the exact same wording, and since the feat is about demoralizing, it is safe to assume that the feat allows demoralize to stack like normal fear (except only with itself). So demoralize could be used to cause a demoralized shaken creature to become frightened, or to cause a demoralized frightened creature to become panicked. It could not cause a demoralized panicked creature to cower. It would only cower if it became unable to flee.
So, you've misinterpreted "cowering" as another fear level but it is not. Cowering is an action you take, seemingly only while panicked. It's not mechanically defined, but it seems that under normal circumstances one only cowers when they're panicked and cannot take any other actions to be able to flee and are cornered. I think essentially it might make you helpless, but as far as I can tell cowering isn't actually defined in game.
Your interpretation from your second post appears to be correct, that while using Soulless Gaze to increase increase fear levels you could cause them to reach panicked, but this would not automatically cause them to cower.
Becoming Even More Fearful: Fear effects are cumulative. A shaken character who is made shaken again becomes frightened, and a shaken character who is made frightened becomes panicked instead. A frightened character who is made shaken or frightened becomes panicked instead.
Directly from the official SRD. Note the absence of specifying anything coming after panicked.
Additionally, Cowering is listed separately within the glossary; much closer to other conditions such as dazed rather than in the fear subset of conditions. By this consideration, Cowering is not a fear-based condition, even though the primary way to gain it is to already be panicked.
but as far as I can tell cowering isn't actually defined in game.
Cowering: The character is frozen in fear and can take no actions. A cowering character takes a –2 penalty to Armor Class and loses his Dexterity bonus (if any).
Thanks for the responses. I misinterpreted cowering to be a fear condition. Disheartening display and signature skill (intimidate) probably led to my confusion. Interestingly, the panicked description says that a cowering creature can use total defense, but the cowering description says it can't take any actions. Not like it really makes a difference at that point, though.