Yes and no.
In a normal case without all this media hype? GZ would have a slam dunk self defense case according to the currently released public evidence without a need to go further than the evidence of two eye witness testimonies that were not GZ. Both testimonies place TM on top of GZ hitting him and both are on record stating GZ was the one asking for help before the shot was fired. That right there is enough in a self defense case normally.
But because of the media and political circus that surrounded this case, the defense team has to make sure it is 100% covered from every angle. They are looking to PROVE innocence in this case where normally that is not needed. Since evidence, beyond GZ's testimony, is lacking of who started the fight, the defense is looking for character evidence to further bolster the self defense claim. With character evidence, oh which the judge said could be used, the defense team is looking to provide even further backup evidence to GZ's claim of who attack whom first. It is circumstantial to a point, but circumstantial evidence can be used in court in the right way.
This is why the defense is going after Crump. They are trying to provide and find evidence of witness coaching/tampering in the case of Dee Dee. They are looking for evidence in TM's past records to see what his RECENT character was. If the defense can provide evidence, even if it's just additional circumstantial evidence, of TM's recent propensity for either violence, criminal mischief, or both; and evidence of Crump's tampering with witness testimony then the defense is going to blow the prosecutions case out of the water. They will be able to prove with as much certainty as they can with the evidence that is available GZ's innocence beyond a doubt. That is the game plan that I can logically deduce.
Even if the above circumstantial evidence is not found, such as a record of TM's propensity for violence or criminal mischief, that doesn't mean the prosecution has a case with the current evidence they have. The point is to prove to the PUBLIC beyond a reasonable doubt that GZ is innocent so that he can get on with his life after this trial once found innocent.