When I'm reading an ingredient list, I'm looking for the absence of dairy, egg, honey, insect products, etc.
One trick I use to make label reading faster (so I don't waste time reading labels for unsuitable products) is to look for cholesterol. A vegan product will never have cholesterol. But, not all cholesterol free products are vegan.
So basically, I check the cholesterol, and if it's 0, I read the ingredient list to see if it's really vegan. If there's cholesterol, I put it back on the shelf and don't bother reading the list. It's a time saver in the grocery store for me. ^^
I think Duncan Hines cake mixes are vegan if you use an egg sub when you make them, but I couldn't swear to it.
We see the world as "we" are, not as "it" is; because it is the "I" behind the "eye" that does the seeing.