Not 100% sure, but I think the rules are that Senators are not allowed to give [unlimited] floor speeches during the trial. They can mainly pass written messages.
Senators will only have the opportunity for limited speech at the trial. Members should refrain from speaking to neighboring senators while the case is being presented.
Pages will continue to be available to relay messages outside the chamber, and the pages also will be responsible for relaying senators' written questions to the chief justice through the staff of the parliamentarian.
A paper on the 1999 impeachment also says "no".
Because the trial consists primarily of the parties
setting forth their positions, during those presentations Senators serve
primarily as non-speaking listeners preparing to render a verdict, and
the proceedings go ahead without requiring their unanimous consent.
Deliberations occur, but in ways that reduce minority resistance rights.
The minority Senators do not have the right to stop the proceedings by
extended debate. They cannot filibuster. The majority does not need
sixty votes to move the process along by cloture as with legislation facing a filibuster.
Alas its references for these points are indirect (to other papers) rather than directly to Senate rules.
A recent article in Politifact says the same
Per constitutional mandate, Roberts presides over the trial. But he is not an all-powerful force, because a bare majority of senators can overrule him. All it takes is 51 votes to change the rules, assuming all members are present. (Under the rules, filibusters are effectively barred.)
Of course, by 51 votes the could also dismiss the trial altogether, so changing the rules to make it some kind of stalemate seems improbable. (Apparently those 51 votes to dismiss don't exist, so it seem unlikely that votes to change the rules to a stalemate effect would exist either.)