http://homepages.wmich.edu/~mcgrew/Evidence.htm
What is not considered, to my knowledge, in the discussion about the Argument From Silence applied on the epistles about the HJ-historicity, is the possibility of a contrast of the kind described above.
Paul comes rapidly to mind as example of someone who didn't mention the historical Jesus. And Josephus also.
The total falsity of the Testimonium doesn't affect the case.
But if the Josephus's Testimonium is genuine, then he is positive evidence of an outsider who mentioned things not mentioned by an insider.
Could an outsider mention what an insider didn't mention?
I find here the real force of the Argument From Silence applied on Paul about the HJ.
To defeat the threat of this so strong Silence, the historicist has to show real evidence of a HJ in Paul. I.e. evidence that would persuade about the historicist view of Paul insofar the partial authenticity of the Testimonium would persuade about the historicist belief of the his author.
The problem is that I can't use this argument since there are serious doubts about the authenticity of the entire TF.