This answer to What would happen if Senators boycotted the Impeachment Vote points out that the Constitution does not compel Senators to vote in an impeachment trial:
The Senate shall have the sole power to try all impeachments. When sitting for that purpose, they shall be on oath or affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no person shall be convicted without the concurrence of two thirds of the members present.
Is there any historical precedent of a U.S. Senator not voting in an impeachment trial (for any kind of office)?