Impeachment and Senate Trial

When the House impeaches an official, does the Senate have to act? The Constitution does not directly address this question, but Senate rules do. Matt Glassman:

These rules strongly suggest that the Senate does not have any discretion in starting a trial upon the appearance of an impeachment article from the House. The use of the word "shall" is pretty clear. pic.twitter.com/QsxWW1x4KI

— Matt Glassman (@MattGlassman312) September 29, 2019

But, but, but...

One-liner: The Constitution does not require a trial. Current Senate rules do require a trial. The Senate could unanimously ignore those rules. A majority could change those rules or otherwise dispose of the trial. A change/disposal would require at least one recorded vote.

— Matt Glassman (@MattGlassman312) September 29, 2019