I would think that
Amit's popularity had something to do with Indian singer and film star
Amit Kumar, whose career seems to have taken off at about that time. Immigrants from South
Asia in the USA still pay a lot of attention to Bollywood films and these influence their name choices.
http://www.amitkumarfanclub.com/index.php
Angelique's original popularity was probably just as a "different but not too different" alternative for
Angela. Its bump up in 1992 was perhaps affected by the characters called
Angelique Collins on the "Dark Shadows" remake and
Angelique Marick on the daytime soap opera "All My Children", along with the worldwide release of singer
Angelique Kidjo's first hit album.
http://www.kidjo.com/
http://darkshadows-resurrected.com/