The Refresh effect from this piece is activated when your Base HP + HP from visible gear (weapon, shield, ranged, ammo, head, body, hands, legs, feet) is above 85%. If you have HP+ gear in your non-visible gear it is not factored into the equation and therefore your latent will kick in when you have less then 85% HP.
To keep things simple lets say from base HP and visible gear you have 1000 HP.
1000 * .85 = 850
850/1000 = 85%
The refresh effect kicks in when your HP is >= 850
Now lets add a Gigant Mantle, BQ Ring and 2x Pigeon Earring +1 for a total of +205HP from gear that is not visible on your character.
1000 HP (from above)
+205 HP from new gear
=1205 HP total
from the previous calculation the refresh effect will kick in above 850HP
850/1205 = ~70.5%
While there may be a minimum total HP percentage that the Parade Gorget latent kicks in at you get the point of how it works.