2 U.S. Code § 30b specifies certain Senate procedures involving Senators objecting to proceedings. (It appears that the intent was to make it clear which Senator was doing the objecting.)
There is a note on this statute which says:
Pub. L. 110–81, title V, § 555, Sept. 14, 2007, 121 Stat. 774, provided that: “The Senate adopts the provisions of this title [see Effective Date note above]—
“(1) as an exercise of the rulemaking power of the Senate; and
“(2) with full recognition of the constitutional right of the Senate to change those rules at any time, in the same manner, and to the same extent as in the case of any other rule of the Senate.”
So, given that this is not (and cannot be, constitutionally) binding on the Senate the instant they don't want it to be, why was this made a statute as opposed to a normal Senate rule?
At first I thought it was because it was part of the larger law mentioned by the note. However, that law actually directly modified or added several other House and Senate rules not in the statutes. So that alone doesn't really explain why this particular provision was given different treatment.