WASHINGTON — As President Trump’s Senate impeachment trial stretched into its third day on Thursday, the Democratic prosecutors arguing the case for his removal played a video clip from 1999 of Senator Lindsey Graham, now one of Mr. Trump’s staunchest defenders, contradicting a central tenet of the president’s legal defense.

Senators craned their necks from their seats to catch a glimpse of Mr. Graham’s reaction to having his words used against him, but he was not at his desk or indeed in the chamber at all, and his seatmate was left patting his empty chair.

The absence of Mr. Graham, Republican of South Carolina, illustrated an emerging reality for senators as they attend a constitutional proceeding with heavy political consequences: Even when you are one of 100 people weighing the fate of a president in only the third such trial in the nation’s history, restlessness can set in.

“We’re doing our best,” said Senator Kevin Cramer, Republican of North Dakota. “With each break and with each disruption if you will, to the sitting in the chair, there becomes a little less discipline.”