Guild Wars 2

So, say you are, for instance, an Engineer, and you have a sigil of fire on your shield. Will this effect procc on the normal auto attack along with the mainhand, or only with skills that makes use of the shield? Moreover, does both carry over to kits?
Heck, do they carry over to weapons that are not technically equipped at all?

Yes to all.
If you have a sigil of fire on your shield, it will proc even using your grenades.

I use Sigil of Torment in my shield to proc with my nades.