I'm not a chef, but, I'd try to analyse them in a number of ways.
Visually first, look at if there are leafy green herbs in it, or bigger chunks of pepper, salt granuals, white dried garlic perhaps, chili peppers or paprika dust. If it is ground fine, what is the overall color and what herbs or spices could that be? Is it a fine dust or a grind or different shaped particles?
I'd taste it a number of different ways and again make a list of what it might be.
Taste it raw--is it salted, peppery, herby, spicy?
Cook it with a little water--taste it, same questions, what could be in there? Smell it, what do you smell, what are the types of aromas? Is it specific to one ingredient, like garlic, or pepper or? Taste it on the front and back of your tongue.
Cook it in a little oil--taste it, same thing.
In each tasting, what are the smells, is it a little like stuffing, it might have some sage in it, does it smell flowery, maybe it has marjoram or thyme, is it oniony, that could be onion dehydrated or garlicy or chive like?
(I'd probably ask friends or family to help with the tasting and listing of possible ingredients with me.)
Then I'd take my lists of most likely characters and mix some spice/herb mixtures of my own to try to get something similar.
Taking it to Penzey's is a great idea too especially if you have a limited spice rack.