Thanks to a friend on IM who suggested I look under synonyms like "Thief", "Steal" and "Flickering lights" instead of Fire. The latter yielded the answer.
This film is called Anna to the Infinite Power. Wiki, IMDB, Amazon
Summary: Anna Hart was always an odd child, a genius, a shoplifter, desperately afraid of flickering lights, with strange prophetic dreams. Simultaneously, several strange things begin to happen. A strange, mysterious neighbor, by the name of MacKayla moves in next door to the Harts. And, most frightening of all, Anna sees her exact double on the television one night. As her investigation of the other Anna, Anna Smithson, progresses, she begins to learn the truth. The truth about a woman named Anna Zimmerman that has been dead for twenty years, and most importantly, the truth about herself.
The film's evil scientist was played by Jack Gilford which clearly explains the reason that the villain was not very imposing to my teenage mind when viewing. An actress named Donna Mitchell played the Piano Teacher to respond to the question in the comments.
Apparently I managed to forget the entire "Clone" part of the story. Upon reading the summary, the memories came back a bit stronger.