He will be neutral but it doesn't really matter who the "presider" is.
If he's neutral, in his role as presider he can coerce the Senate into calling witnesses and otherwise observing the formalities of a fair trial. With even minimal backing from a few Rep Senators, he can establish a secret ballot.
The witnesses will probably do lots of damage to Trump, and highlight the absence of Trump's testimony. And as soon as a few Republicans can vote or abstain without identifying themselves, Trump's odds of conviction go way up.
And no, gerrymandering didn't win Trump the election.
It probably did. The stats say it did (70,000 + missing Presidential votes in Michigan, almost all of them from gerrymandered Dem districts, never even investigated, for example).
It set up the voter suppression and infrastructure manipulation, the ID requirements, the use of dubious and easily exploited voting machines, the failure to audit suspect vote counts, the invalid purging of voter registration rolls, and so forth, in the key States that Trump narrowly won.
Oh, we all know that unprecedented use of budget reconciliation was the ONLY reason Obamacare passed. That's how underhanded the Democrats are.
Nothing secret or underhanded about it - not since 1980, near forty years ago.
It wasn't unprecedented, either; it had become frequent, as Republican hyper-partisan tactics - especially the use of the filibuster as never before - increasingly dominated Congressional politics. After the election of 2008 Republican Senators were even filibustering
their own bills, if you recall, to prevent anything approved by Obama from getting through the Senate.
That's what "unprecedented" looks like. Filibustering one's own bill.
Meanwhile, reconciliation is not all that difficult to beat in theory - from Wiki:
Senators could theoretically prevent passage of a reconciliation bill by offering an unending series of amendments in a process known as a "Vote-a-Rama," but, unlike the modern filibuster, senators introducing these amendments must stand up and verbally offer the amendments.
All it takes to beat reconciliation is a few Republican Senators with the principles they claim instead of the toadying and cowardice they display.
Which is too high a bar, of course, but the theoretical possibility is there.