Automatically generate different timeless random numbers in duplicate effects on the same layer

If I want to automatically generate a different timeless random numbers on each instance of a duplicated layer, I know how to do that by referencing the index. For example:

seedRandom (index, true);
random ()

What I need to do is similar to that, but I need the different timeless random numbers to be generated in duplicated effects on the same layer.

Obviously, using 'index' won't produce different random numbers between the duplicated effects because the layer number will be the same for all instances of the effect. Instead, what I need is some way to either self-reference the effect name/number, or randomly generate a timeless number without specifying a seed. See what I mean?

Any suggestions?

Thanks!