Rule 16L applies in part here but not when both players arrive at the board at the same time. When White and Black arrive at the game table at the same time, does White decide on which side of the board to sit for the game?
RULE CITED
16L. Possible stipulations.
The director may require that clocks face a certain direction or that Black or White sit on a particular side of the table. In the absence of such a requirement, unless Black is late arriving for the start of the game (39A1), Black
determines which side of the board the clock is on, and the player arriving at the chessboard first may choose either side of the table to sit on. See also 39A1, Black player late.
39A1 Black player late.
If Black is late for the start of a round, White makes the choice of equipment. Unless announced or posted otherwise, White may also choose which side of the board the clock is on and which side of the board to sit on. Black may not object unless White’s equipment is non-standard or White has not complied with any special announced or posted stipulations (16L), in which case Black’s clock continues to run. Again, the final decision is up to the TD in questionable cases.
If both players arrive at the same time and the two players really can’t sort it out between themselves, I would defer to Black given they get choice of equipment and clock placement so I would argue this ruling is analogous to other rules (1A).
PS - It really is time for US Chess to add Chapter 3: Chess Notation and Chapter 4: Equipment Standards to the free online rules available.