This trinket procs even when not equipped. Had this just sitting in my bag and was doing parses with my live gear (I don't even have HK gear) and noticed in the parses this was activating. Over the course of 5 separate 3minute parses it did about 4800 damage on single target dummy, and 22,800 damage on the AoE triple dummy. Adds a good chunk of dps (6% on single target) for something you don't even have equipped. I tried putting it and the weapon in my bag, and it still procced. Then I dropped both items and the proc persisted.
I was using Dhel's Spear of the Beast in my main hand and Challenge of Rivals in my trinket slot.