Jimmy drowned his sorrows by killing people for a while, but by early September, six weeks after last seeing Ethel, he wrote her a letter.

To the police of NSW
My dear Ethel.
You did not now suppose you was free, dear, when you was with me; you never think that you was at home. I have been good to you, and often say the Lord take me away. I hope he got you. You know you are going fast, dear. I suppose you glad, but I am not. I feel sorry for you, dear Ethel...

He asked for her to come and spend some time with him before he gave himself up to the police, but she did not go.
Either she feared for her life, possibly knowing that under tribal law Jimmy could kill his deserting wife, or the police would not let her.
The police would want to protect their chief witness and would not want to do a deal with an outlaw with a price on his head.