Sisnando ben David Davidiz Davidiz, Vizier of Castile, Emir of Toledo, Comtes de Quimbra - Evidence for parentage?

Hello,

Does anyone have any evidence for the parentage currently attached to Sisnando ben David Davidiz Davidiz, Vizier of Castile, Emir of Toledo, Comtes de Quimbra Abu Suleiman David ibn Yaʿīs̲h̲ ben Yehuda Ibn Ya Ish ben Zakai II ben Zakai II, Nasi, Qāḍī, haDayyan of Toledo and Shoshana I am not finding anything about his parentage, let alone evidence beyond the Jewish-sounding name "David" that he was of Jewish origin.

If anyone has any evidence for these connections please come forward, otherwise, I will be disconnecting the relationship.

Sincerely,
Tamas Caldwell-Gilbert