I didn't exactly say that ぴかぴか comes from ひかり (originally pronounced
pikari), but rather that ひかり itself seems to be 擬態語. That is,
pikari may come from
pika which may have been used to mean 'shining' back in the old days just as it is today.
I don't have time now to search for the etymology of the specific words you gave me here, but as far as I can tell, it is hard to find a root word for most 擬態語, and it seems like many of them are, in fact, sound impressions that have been subjectively attached to non-auditory phenomena (such as light or feelings).
Curiously enough, it turns out that いらいら might be one of these 擬態語 that actually originate in a word: いら (written 刺 or 苛) appears in Classical Japanese in the meaning of a thorn (the same as とげ in modern language, apparently), and it probably also includes small toxic hairs as those on the Japanese Nettle (イラクサ). So いらいら obviously comes from the irritated (See the similarity? That's a nice one too :)) skin you get after being stung by a thorn or a nettle.
As for きらきら, we'll probably never know. This ideophone is almost as old as you can get with Japanese: it already appears in 宇津保物語 (Utsubo Monogatari) as part of the verb きらめく, which maintained the same meaning to this very day.