Doing some research today. I think I may have found what all of the TKMGK letters stand for.
T --THULLAI-- K --KOJIN-- M --MAZU-- G --GAIA-- K --KHRONUS--
Thullai is a Greek air demon. Kojin is a Japanese Fire God. And the God of the Kitchen. Mazu is a Tebetan Goddess of the Sailors. Gaia is a Greek Mother Earth goddess. Khronus is another Greek God known as the Castarator and the Father of all Gods.
T is for AIR. the first K is for FIRE M is for WATER G is for EARTH and the last K is the huge SWORD Ayamu must draw from the stone when he has brought all the pieces together for it.