Lord Muruga and Guru

The meaning and symbolism of Lord Muruga (or Skanda, Shanmukha, Kumaraguru, Vadivela etc...) has been intriguing me for quite a long time now. Just like Ganapathi or Ganesha stands for the Mula Chakra and Elephant becomes the symbol for the root chakra, I am led to believe that Skanda is the symbol for Ajna chakra. Again, a very vain and poor explanation - just that I am intuitively tugging at this...

It seems Arunagirinathar received his mantra diksha from Murugan in the form of a Guru. Sri Muthuswamy Dikshitar uses the mudra "Guru Guha" in his kritis. Murugan as Swaminathan - he gives upadesam to his father.

Say Om Guru Guha continuously - and you will hear Muruga!

The term Shan-mukha - is it then for the 6 centers from Mula till Ajna?
Is it symbolic of 6 branches of Vedic learning - Shan-matham as Kanchi Periyava says.
Is the Vel really nothing but the Guru's direction and mantram?

Then what is the explanation for Valli and Deivanai? If they merge with Murugan who is at Ajna - will they be symbolic of the two major nadis - Ida and Pingala?

What is the meaning of Guha in Guruguha - is it guhya - that is secret. The secret Guru within?

And, why is Murugan the son of Shiva and Shakti....is it because he represents the Ajna - the one just next to Sahasra which is the abode of the Universal Father and Mother? And, if Shiva burnt Manmatha to ashes by opening his third eye and the result was Skanda....it more so points to Skanda as a symbol for the third eye!
Subrahmanya is the knower of Brahman - again "intuitive knowing" happens at the third eye.

Could it just be that the entire ensemble of symbolism in Murugan worship is nothing but trying to open the third eye of the devotee? Of course, better worship Ganapathi before embarking on the journey, as nothing happens if one is just stuck at the root.