Why might the Lawson minimal surface $\xi_{1,2}$ have a Morse index 9?

In page 15 of the article New Applications of Min-max Theory, Andre Neves said that: a wishful thinking would suggest the Lawson minimal surface $$\xi_{1,2}$$ in the 3-sphere to have a Morse index 9, but there is no real evidence.

My question is, what suggests the index to be 9? Say, can we find a 9-parameter deformation of $$\xi_{1,2}$$ which decreases its area?