@hightor,
Good question. I have no idea whether there is a rule in place that necessitates a vote or what time frame might be mandated.
Of course, if they don't bring it to a vote, that leaves the door wide open for the right to yell loudly that the Dems aren't because there's no evidence and it was all a farce.
I'm also not sure in the ways that McConnell is constrained in ways that would damage his goals. So I don't have a clear view of how a Senate trial itself (not conclusion) might work damage on either side.