There has been a lot of confusion about sigils lately, and not without reason - the game really doesn't give you much indication about how they work, especially when there's more than one of them involved. The most important piece of advice to give here is that it's easy enough to test all kinds of combinations for free by going to the Heart of the Mists and fighting Target Golems or Conquest NPCs. Most of what I'm writing here I've gathered from my own testing in the Heart of the Mists, and it's important to note that sigils may work differently in PvE/WvW than they do in sPvP, though I have seen no evidence to suggest that this is the case. Moreover, the situation may change with future updates to the game, especially since some of the following behaviours may not have been intended.
Before I go further, I'll address a common misconception the idea that when holding two weapons, each sigil only affects the skills that involve that weapon. This is simply not true; any and all sigils take effect regardless of which weapon they are located in. However, only the sigils in your current weapon set take effect - sigils in your second set only take effect when you switch to that set.
The main aim of this guide is to detail any and all caveats in how sigils work, especially when used in combination. Broadly speaking, there are five major categories of sigil; I'm grouping these by the different ways they behave.
(1) Passive effect, e.g.
Superior Sigil of Force (+5% damage)
Superior Sigil of Venom (+10% poison duration)
(2) Stack on ****, e.g.
Superior Sigil of Bloodlust (+10 power per stack; max 25 stacks)
Superior Sigil of Demon Summoning (summons a fleshreaver on the 26th stack)
(3) Effect on critical, e.g.
Superior Sigil of Fire (30% chance of flame blast on crit; 5s ICD)
Superior Sigil of Strength (30% chance of 10s might on crit; ~1s ICD)
Superior Sigil of Water (30% chance to heal nearby allies on crit; 10s ICD)
Superior Sigil of Earth (60% chance to bleed for 5s; ~2s ICD)
(4) Effect on weapon swap, e.g.
Superior Sigil of Battle (3 stacks of 20s might on swap; ~9s ICD)
Superios Sigil of Hydromancy (AoE 3s chill and AoE nuke on swap; 9s ICD)
(5) Effect on ****, e.g.
Superior Sigil of Speed (10s swiftness on ****)
Superior Sigil of Restoration (Gain health on ****)
(1) Passive effect
In general, passive effects work fine in conjunction with one another, or with any other type of sigil. The only exception I've seen is that 2 Sigils of Force don't seem to give any additional damage over 1 Sigil of Force; I suspect that this would also happen for the Sigil of Accuracy, but this would be much more difficult to test.
Also, on equpping a Sigil of Accuracy the critical chance will not show up in your character's attributes window. However, according to ArenaNet, this problem is only with the UI; the chance increase does actually take effect in-game. Apparently, many other passive critical chance increases, such as the thief trait Keen Observer, also have the same problem.
Further testing needed:
Sigil of Accuracy + Sigil of Force
Sigil of Accuracy + Sigil of Accuracy
(2) Stack on ****
These seem to work fine in conjunction with all other types of sigil. However, it is mostly pointless to use two of these as you can only have stacks of one type at any given time. If you use two of the same stacking sigil, you do get two stacks of the same type on every ****, though.
Also, stacks are preserved until you go down or change zones. Swapping weapon sets and even unequipping the stacking weapon doesn't lose you the stacks.
(3 + 4) Effect on critical or weapon swap
From what I know so far, all type 3 and 4 sigils have internal cooldowns, whether they specifically say so or not. For example, the Sigil of Battle appears to have a ~9s cooldown, similarly to the Sigil of Hydromancy, even though this is not mentioned in the in-game description. Similarly, testing suggests that the Sigil of Earth has a cooldown of roughly 2s, even though this is not included in the description.
Most crucially, any internal cooldowns appear to be shared globally while one sigil is cooling down, another type 3 or 4 sigil cannot activate (Type (1), (2) and (5) sigils continue to work without any problems). In other words, any sigil that has its own internal cooldown cannot activate while another sigil is on cooldown. The most extreme case of this is the Sigil of Rage with its 45 second cooldown this means that for 45 seconds, no other sigil with a cooldown can proc, even if it's on a different weapon set.
If you want to confirm this for yourself, the simplest way to do this in sPVP is to put a Sigil of Fire on one weapon set, and a Sigil of Hydromancy on the other. Keep attacking a Target Golem until your flame blast procs, and then switch weapons the Hydromancy sigil will not trigger. However, if you wait for 5 seconds and then switch, it will. This demonstrates that the flame blast cooldown is in fact affecting the Hydromancy sigil as well.
Similarly, you can equip a Sigil of Fire and a Sigil of Air in the same weapon set, but only one can proc on any given crit, and after that it will take 5s before either of them can proc again.
(5) Effect on ****
I haven't done much testing on these sigils, but from a quick check I found that you can have effects from two different sigils after a ****. You can verify this by killing one of the Conquest NPCs with a Sigil of Stamina and a Sigil of Speed equipped.
It appears that these sigil types do not have any internal cooldowns; testing by klineshrike indicates that mass area of effect kills with a Sigil of Speed equipped can stack to give long (50 second+) Swiftness boons.
Whenever you have a bundle in your hands, your weapon set is deactivated, which means that the sigils from the weapon set become inactive (you lose the weapon's stats as well, though the stacks from stacking sigils remain). Moreover, equipping or dropping a bundle does not count as a weapon swap - this means that weapon swap sigils are useless for an Engineer.
Switching attunement counts as a weapon swap, but "your next attack [...]" type sigils do not work properly. This is almost certainly a bug, and I suspect it's because of the the additional effects that already happen whenever you switch attunement. Sometimes you see the icon in your effects monitor, but for some reason it never seems to work properly.
In other words, Sigils of Leeching, Doom and Intelligence are currently useless for an Elementalist, but Geomancy, Hydromancy, Energy and Battle do work properly. Furthermore, if you're going to use one of these sigil types on an Elementalist, you should be aware that there is a 9s ICD, and swapping with a bundle equipped does not count for the purposes of weapon swap sigils.
This one I haven't tested too much, but I at least know that you can't get sigil crit procs on the crits of your illusions.
Further testing needed:
Sigil of Force and Illusions
Sigil of Agony and Illusions
TL;DR - read the bits in bold
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