Shaivism has really mysterious origins. Of course, the colour of Shiva is not one of them, as I think Shiva's human form might be very recent. White phallus of Shiva in Kashmir is just a random natural phenomenon than a normal phenomenon. (Note: Please refer Wikipedia for all the unknown terms and concepts, I'll try to insert the links later).
Why Shivism could possibly have only Northern origins?
In one my previous posts, I speculated that goddesses might be the main deities of pre-Indo-Aryan matrilineal Dravidian Indians with phallus having a minor role in the broader scheme of the things. However, under the influence of patriarchal Indo-Aryans the phallus could have become powe ful in North Indian society.
A powerful testimony of the prevailing situation during those times could be found in Tulu/Malayali socities that practiced/practicing matrilineal system. Matrilineal systems are one of the oldest and derived from the primitive social organizations. In Malabar many castes have their own goddess temples and their own priests. They could consecrate the temples without any Brahmin intervention. However, that was not the case with Shiva temples. Probably, Narayan guru was the first person to defy Brahmin hegemony in consecrating Shiva temples in South India. Therefore, in Brahmanical Hinduism societies Shiva is part of Vaidik religion. The question is who are those non-Brahmancial Shaivites in South India.
Agama Shaivism and Vaidik Shaivism:
From my understanding the difference between those two was that the former was a Dravidian tradition accommodated Vedas, the later was an Indo-Aryan tradition that accommodated Shiva. However, we need to have a deeper understanding of Tamil Nadu Shaivism and Karnataka Shaivism. Unfortunately, my knowledge is limited at present.
I have read that the Shaivism in Tamil Nadu was an import from Kashmir. Interesting point is it came to South not as a part of Brahmanical religion. The present day Kashmiri Pundits might have a very complicated history of transition from Shaivism to Brahminism. It looks like the Shaivism that reached Tamil Nadu also brought Vaidik literature along with it. So it was not Brahmins who first brought Vaidik literature to South India.
In Tamil Nadu Shiva temples, Shivacharyas are the hereditary priests and even Brahmins donot have priestly privilieges there.
Are Vedas part of Shaivism and Shaivism part of Vaidikism?
The first part of the question is pertinent in Karnataka. Here, Veerashaivism rejected Vedas. In Tamil Nadu Vedas were part of Shaivism though not supreme. The question is who brought Shaivism to Karnataka. What is the origin of Jangamas(Shaiva Saints)? (note: Veerashaivism became Sanskritised in the later period)
The second part of the question lies in Vaishnava movement of Ramanujacharya. It seems Vaishnava movement did not accept Shaivism as part of Vaidik religion. This was one of the main divisive point between Shaivites and Vaishnavites in Tamil Nadu that led to Vaishnavites flight to the region of Karnataka. Why did Ramanujacharya consider Shaivism a non-Vaidik religion? Was supremacy of Vedas uncompromisable for him? Shankara before him declared Vedas were supreme and still remained part of Vaidik Shaivites. What was the position of Shivacharyas in Tamil society vis-a-vis Tamil Brahmins? Why were Vaidik and non-Vaidik Brahmin distinction there in Kerala society? At present I have only questions.