Do items that grant skills with long cooldowns trigger the cooldown upon equipping/enabling the skill?

As an example: Guardsman’s Spoulders
With the skill: Guardian’s Will

It is similar to menhirs will, with fixed 5s duration and 45s cd, triggers on 35% life so 2% above menhirs will.

Condition: Requires Shield

Scenario:
I use these shoulders.
I use a 2hand weapon most of the time, and switch to 1hand + shield occasionally.

Observation:
After switching to 1hand + shield, I got hit hard and menhirs will triggered (33% life trigger), but I could not see any other skill being triggered (item skill should trigger at 35%).
=> It looks like the skill did not trigger.

Question: Upon either equipping the item, or in this case, reaching the requirement for the item skill to work, the cooldown is triggered silently (no icon no nothing).

…so, did I just not see the icon? Is there no such icon? Or does it indeed trigger the cd silently?
Anyone knows?

guardsman will is a green/aether coloured version of menhir’s will icon

edit, after a quick test def seems like it works on swap
it’s possible you didnt’ change fast enough so was below/past the trigger condition

turns out you can’t be “below” the trigger point, unless dead, so it might be you didnt’ change fast enough and got above the 35%trigger condition, and then went to 0
gets hit, gets healed(above 35%) quickly, swap now in effect, dead or such(goes from +35->0 in a “single” hit)

as long as not actually dead i could even wait until below 35%, swap weapons, and guardsman would still trigger/heal me/i didn’t have to go through the threshold itself but just be under it
(but i also didnt’ have menhir to support heal)

Likewise there seem to be a strange low hp wiggle-room threshold where even if below 35% it wont trigger if still low enough HP
(consistently died going from +35% → 1-2%, despite not insta dying/being a live a few mili secs on 1-2% hp)

Weird…

Thanks for the info though, I guess I just overlooked it, will try to pay more attention next time.