When it comes to trial ...
OK, here's a thought.
When (I'm going to go out on a limb and say when) the impeachment of Donald John Trump goes to the Senate for trial, that trial will be presided over by the Chief Justice of the Supreme Court - John Roberts. That's what the Constitution says. That's ALL it says. That would appear to leave a great deal to the discretion of the justice in question.
Being a Republican, Chief Justice Roberts can't be expected to be completely impartial, but he has in the past appeared to care about his legacy. It's not out of the question that consideration of his legacy, and of how appearances could affect it, might assist him in making some of the decisions on how to preside at this trial.
What would happen to the reputation and legacy of a trial judge in the courts who allowed accomplices of an accused in the crime for which he or she is on trial to sit - and vote - on the trial jury?
Of course the Chief Justice cannot kick people out of the Senate, but he may be able to remove them from the proceedings. At the very least I would think he could require those Senators to recuse where there is evidence that they have involvement in or knowledge of (prior to the hearings). IANAL, but I don't think that involvement or knowledge would have to be proven beyond reasonable doubt, since what is at stake is the integrity of the trial - and avoiding any appearance of evil - not any penalty or other negative consequences to those Senators.
Senator Graham's opening of an investigation into the matter that is the nexus of the crime makes it obvious he should refuse. #MoscowMitch did not earn that hashtag for nothing. I don't watch Fox News (except in short clips on the internet, and very few of those; essentially, just enough to learn that Napolitano generally speaks solid truth and one or two others do occasionally), but I am sure there are Senators who have said things there which could lead to their being "requested" to recuse. Mike Lee of Utah, Ron Johnson of Wisconsin, Ted Cruz of Texas, Tom Cotton of Arkansas and John Kennedy of Louisiana, and some others, apparently attended a White House meeting with Trump to work with him on strategy for his defense at the potential trial. That doesnt sound like the conduct of impartial jurors.
I don't know what the best method would be to pursue this - a petition directly to the Chief Justice? A nod to Democratic members of Congress to bring it up to the Chief Justice? Possibly just a tidal wave of publicity on the implications? And I would definitely not be competent to draft such a request - that should be a lawyer or at the very least someone with a strong legal background.