I'm not quite sure this is spoiler talk, given its first season stuff we're discussing. But to be safe I'll tag it like you did.
Spoiler: Click here to viewI'm pretty sure when they talked about the eclipse this season they just said that the abilities were starting to be heavily documented after the eclipse.
Not that the eclipse made them have their abilities. In fact, it may have done the same thing as it did this season, blocking their powers all together. I don't think anything happened during the eclipses of the past, so thats a very good possibility, I believe.
Honestly, the more I think about it, the more I think that Mohinder only started documenting and finding people with abilities after the eclipse the first season; the eclipse may have prevented some powers from manifesting, though some already had (Claire said her first video we saw was her like 7th attempt, and her power to hea herself had been in effect her whole life...others had powers well before the eclipse as well) and so when the eclipse went away it could have just awakened them. That's probably it.