The complete answer to your question is found in "Dancetime, 500 Years Of Social Dance, Volume 2: 20th Century." The Apache is performed, among The Castle Walk and many other dances, to music by Dance Through Time. The Video can be purchased on www.dancetime.com
SHERIFF

I have an old print by a French artist - Louis Icart - that is entitled Apache Dancer. It's from the 1920s-30s. The scene is some dark and sinister back room, probably a brothel. The woman is wearing a dark dress with a vivid red "apron" over it, and she's giving a come-hither kind of look to a shadowy man. I was fascinated by the print when I was little.
Anyway, the Oxford English Disctionary (the big 26-volume version) has an entry on the Apache. I don't have the OED at my disposal right at this minute, but from what I remember, they described it as dance that protrayed violence.
I'll check it the next time I'm at the library.

I've checked a couple of sources: "apache" is a reference to the ruffians of the underworld of Paris. The dance was semiacrobatic, performed as a duet, and was used in vaudeville. It came to the USA just after the First World War. But I haven't run across any information about figures, music, timing or things like that.