Sentence:  "Testing the waters" is a veil for what candidates do in the years when it's too unseemly to be seen actually running for president. . . . But this veil is dropped when candidate and handlers believe the coyness has begun to cloy. And then the candidate's <WSD>dance of the seven veils</WSD> has begun. 
Meaning of the word marked with <WSD> tags:  The incremental disclosure of tantalizing bits of information.