Does the headlamp accessory help for missions like 9 - 2 Alone in the Dark because that would be pay to win.
Frosty Headlamp
Yes, that's the one. I saw someone wearing it and noticed it was giving off a lot of light. I did not mean to single out Frosty Headlamp users, just that the player I ran into had a Frosty. Do they all shine so bright? Though that webpage you linked to mentions the existence of a hat with a built in Headlamp available for 150 crowns in the Haven Bazaar, which should balance it out since even the poorest players should be able to afford 150 crowns by spending 5-10 minutes begging for money near the auction house. It just means they have to embarass themselves by wearing a 0-star item while the pros can put headlamps on their 5-star helmets, which honestly isn't too bad when you think about it.
"Does the headlamp accessory help for missions like 9 - 2 Alone in the Dark because that would be pay to win."
No. It's just a headlamp accessory that only helps your knight look like a lighthouse.
Do you mean the frosty-themed item at this page?
https://wiki.spiralknights.com/Headlamp
Is there a reason why you aren't concerned with other headlamp accessories?