The Ineligibility or Sinecure Clause (Article I, Section 6, Clause 2) states:
No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States, which shall have been created, or the Emoluments whereof shall have been increased during such time . . . . (emphasis added).
Here and elsewhere, the Constitution of 1788 distinguishes "appoint" from "elect." Whether or not contemporaneous popular usage did that too is an entirely different question—just as legal usage sometimes differs from popular usage.
