Curious if she has a connection to the sun? Would be appropriate if she was, as Louis XIV was called the "Sun King".
Yes she has. Her original figure, Prince Shōtoku can some times be referred to as "日出処の天子" (The prince/king/emperor of the sun rising land). And her title ”日出処の道士”was a parody of that reference, meaning "The taoist priest of the sun rising land" (or rising sun land? same meaning though). So yes, she has connection to sun in her nature.