The Shatapata Brahmana Section 2.6.2 mentions something very interesting:

  1. He offers 1, with the text (Vâg. S. III, 57 a), 'This is thy share, O Rudra! graciously accept it together with thy sister Ambikâ! Svâhâ!' Ambikâ, indeed, is the name of his (Rudra's) sister; and this share belongs to him conjointly with her; and because that share belongs to him conjointly with a woman (strî), therefore (these oblations) are called Tryambakâh. Thereby, then, he delivers from Rudra's power the descendants that have been born unto him.

Now this is the first time I have heard of Goddess Ambika being mentioned as Rudra's sister. BTW the meaning of Trayamabaka is also different from what we traditionally assume. The footnote mentions:

aitt. Br. I, 6, 10, 4, this sister of Rudra is identified with the autumn, wherewith the god is wont to kill (viz. by means of catarrh, fever, &c., Sây.).

If someone has the translation of Aitreya Brahaman maybe they can confirm what is the term used in the same. I want to know why this text calls Ambika the sister of Rudra and if there is a deeper meaning to the verse as hinted in the Aitr. Brahmana