While my probes have netted me more palladium than I'll ever be able to use, I have played through the entire game finding almost no Element Zero.
Is there a secret to finding planets which contain Eezo, or is there just not much of it out there?
Like the other answer, there are lists you can use to find planets for any particular mineral.
If you don't want to use a list, there are a couple of tips:
It's pretty rare, but there are lists floating out there of planets where you can find it. For example, here.
There is no secret. Element Zero is just very rare.
Here you find a list of planets that have Element Zero: http://masseffect.wikia.com/wiki/Element_Zero