Looking for ideas (Chosokabe Legendary): how to make Sogo and Miyoshi fight?

[Maltz]

I am at the beginning of the campaign as Chosokabe on Legendary.
It is now Turn 14. I have Tosa and Iyo (from Kono). Got 4 trade nodes west of Kyushu.

Sogo (of Sanuki) is my ally. Miyoshi is my trade partner. Both are at least friendly to me.
Sogo and Miyoshi used to be allied. But Sogo agreed to switch its alliance to me while dropping all ties to Miyoshi.
So now Sogo and Miyoshi dislike each other.

I thought this is enough reason for them to go to war. But it has not happened yet.
I tried to let the game continue to see what will happen. The two clans will hire a bit more army but will soon max out.
Then their army just stand there, doing nothing.

Any advise on how to make them fight each other, so my army can make things more interesting? :p

Note: My eventual goal is to wait until their main force leave their castle, use my ninja to immobilize them, and incite a peasant revolt to take over their rather defenceless castle. Strangely, when I get a rebel out in Miyoshi's main province with the full stack army still in the castle town, the huge main garrison army did nothing about it. Weird...