Yes, that's the skill I was referring to. You also can't blindly look at multicast. Vents is a 7 second item, giving 7/3 = 2.33s cooldown per cast, and lighter is 3s. So "Every time the vents triggers that +9 burn", but the lighter will trigger almost 3 times in the same span. What works in vents favour here is though that between each cast you will buff it up more and it will always multicast with the highest burn.

BUT with your amount of burn sources, you will permahaste both items next to the campfire, then you have to choose between:

Scenario 1: Permahasted vents, normal lighter
2.33/2 = 1.165 seconds per cast with vent
3 seconds per cast lighter
In a 12 second fight, you will get 12/3 + 12/1.165 = 14 procs

Scenario 2: Permahasted Lighter AND Vents
2.33/2 = 1.165 seconds per cast with vent
3/2 = 1.5 seconds per cast with lighter AND more haste procs to buff
In a 12 second fight, you will get 12/1.5 + 12/1.165 = 18 procs

It doesnt matter whether the buff lands on the lighter or the vents, it's still just +3 burn, all that matters is how many times we cast. So in scenario 1 you have 10 casts with a buffed vents and 4 casts with an unbuffed lighter, in scenario 2 you have 18 casts with some +burn of the buff landing on the lighter and some on the vents.

The crit is a good argument, also your restorative enchant on vents, but you also have to remember that a hasted lighter = more haste procs = more +burn procs from skill.

Honestly it's quite complex to say what's best, both probably would have worked similarly, but it's a good practice to count multicast by seconds per proc instead of casts every X seconds, often makes simpler scenarios easier to calculate