How can you then distinguish between the two non-randomly-answering gods? They will answer the same, and the answer from the randomly-answering god appears to contain no useful information.
Also, I want to thank you again for helping me out with awk/sed/grep/command line stuff, from a year ago!
In the case of this puzzle, a counterfactual can be used to embed a question X within your question Y. By doing so (and exploiting the phrasing of the problem), you force the gods to answer in a manner that either reveals their identity as True, False, or Random.
Explaining the actual process through which the counterfactual is used to solve the problem is a bit tedious but the Wikipedia article on the puzzle has a pretty straightforward explanation of the reasoning[1].
[0] http://en.wikipedia.org/wiki/Counterfactual_conditional [1] http://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever.
I'm guessing the same principle should apply though, I'll comment an update if I don't fall asleep from having been up all night. Thanks for pointing that out, though.