James -- I think you are right. Here is an excerpt from the book "Men with Mustaches and Men Without Beards" by Afsaneh Najmabadi:
"In this intensified visual regime, the sun, evoking the sun king for the Persianate dominion, became intimately identified with the person of Fath'ali Shah. The sun as metaphor for the ruling monarchs (including non-Iranian ones) predates the Qajars, and the expression khawrshidkulah (sun-hatted person) ws common. Although since the early Qajar period, this expression has been used to identify Catherine II of Russsia, in Safavi and early Qajar sources it was applied to any monarch. Aqa Muhammad Qajar, the fouder of the dynasty, was described through a number of sun-related metaphors, such as khawrshid'ara (adorning of the su) and khawrshid'khassiyat (having the same qualities as the sun). But it was the poets and writers of Fath'ali Shah's court who saturated the metaphoric field with the sun king. Two figures in particular delighted in inventing and proliferating sun metaphors for Fath'ali Shah: the court poet Fath'ali Khan Saba and the historian Rustam al-Hukama. Many of Saba's panegyrics center on the notion of Fath'ali Shah as sun. One of his best-known and most eloquent panegyrics, composed for the occasion of welcoming the Persian new year (nawruz) was a comparison between the sun in the sky and the sun on earth, with the opening verse:
Two suns from which the earth and time turned afresh
One entered the palace of hamal, the other the place of Kian."