Reading the responses to your query about Averígüelo Vargas: "it is difficult to investigate", or "Who knows" (the "who" being "Vargas"), I wondered why the phrase should have come to mean this and just who is/was Vargas? ...if even a real person...
My *Gran Diccionario Oxford *was no help:-(
But now having Internet access, I entered the phrase into a search engine to find several items of interest including multiple references to a play titled Averígüelo Vargas by Tirso de Molina. I got the impression that this must be a well-known play from Spanish literature.
I read a synopsis of the play in English, (the actual Spanish text being too long and difficult for me) but although I enjoyed the read, I was more confused after than before. What relationship did the Vargas in the play have to our phrase'...In the play Vargas is a dwarf - no, not really. Vargas is the disguised half-sister of the king...well, the illegitimate...oh never mind, it is all too confusing and, as I said, shed no light on why "Averígülo Vargas" should necessarily have come to mean to investigate something difficult.
And then I happened upon this: http://www.1de3.com/2004/12/12/averiguelo-vargas/
This thread was easy for me to follow in Spanish - maybe I have progressed from beginner to intermediate with that Gran Diccionario, shortcomings or not. Everything seems clear. Francisco de Vargas must be our man!
...and then I noticed a list of other related threads at the bottom of the entry. One reads: "Falsas etimologías (4)"....
Happy for the evening, I won't follow any of those until tomorrow.