Query: Origin of "give/have the willies"

[Cohen, Gerald Leonard]

I've been asked the origin of "willies" in "give/have the willies." OED3 lists it as "Origin unknown."
Would anyone have any idea?

Below is OED3's entry for the item.

Gerald Cohen

[OED3]: 

willies, n.
Pronunciation:   /ˈwɪlɪz/ 
Etymology:  Etymology unknown.
slang (orig. U.S.).

the willies: a fit of nervous apprehension. Chiefly in phrs. to give (someone) the willies, to get the willies.

1896   Dial. Notes 1 427   To have the willies, to be nervous.
1900   G. Bonner Hard-pan 99   It just gives me the willies to think of your being down on your luck.
1913   J. London Valley of Moon 105   Bert gives me the willies the way he's always lookin' for trouble.
1927   H. A. Vachell Dew of Sea 261,   I sure got the willies at the thought of meeting you.
1942   G. Kersh Nine Lives Bill Nelson ix. 57   It can give you the willies when, in broad daylight, you hear a rifle go off.
1953   F. Swinnerton Month in Gordon Square 202   Gosh! She was getting the willies. It was awful.
1962   J. Heller Catch-22 xii. 127   Chief White Halfoat shuddered. ‘That guy gives me the willies,’ he confessed.
1975   B. Felton & M. Fowler Best, Worst & most Unusual 277   You can now visit Winchester House. But we wouldn't advise it if you suffer from the willies.
1984   A. Carter Nights at Circus iii. i. 199   Not that the ‘wagon salon’ isn't very pleasant, if it don't give you the willies.

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