Tergiversate originates from two Latin words: tergum (back) and vertere (to turn).  That turned into the Latin word tergiversat (with one's back turned).  That came to Middle-English as tergiversate in the mid-17th century.  

Tergiversate is but one of a whole family of closely related adjectives, nouns and verbs.

 tergiversate (intransitive verb):

tergiversated, tergiversating

to engage in tergiversation

tergiversator (noun)

 tergiversation (noun)

1 : evasion of straightforward action or clear-cut statement : equivocation

2 : desertion of a cause, position, party, or faith

 tergiversatory (adjective)

displaying or practicing tergiversation

 tergiversant (adjective)

: tergiversating

 tergiversant (noun)

: tergiversator