As the documents establishing (internal organization of) the BASC and the initial flight rules show, these were "mini-agreements" signed within the framework of the Allied Control Council and its specialist sub-committees like the Committee on Aviation of the Air Directorate.
I haven't found a detailed secondary narrative of these negotiations (regarding the air corridors), but one paper mentions...
insisted on interpretations of the directive that the West could not
accept. His demands that the Soviet Union control the air
corridors to and from Berlin and that it regulate the city’s trade
with the western zones were bad enough, but Sokolovsky’s U.S.
counterpart, General Lucius D. Clay, foresaw a breaking point in
the discussion over Russian demands regarding city finances [the Soviet Bank proposals].
So it's clear that the Soviets at least tried to obtain some greater level of control on these corridors during the negotiations than was ultimately agreed upon.
For those willing to dive into the primary sources, "extracts" of minutes of the meetings are also available. The "Proposed Air Routes for Inter-Zonal Flights" were discussed at a top-level meeting of the Coordinating Committee (meaning Sokolovsky, Clay etc. were present) on November 27, 1945. This meeting concerned the more detailed "Report of the Air Directorate on the Creation of a System of Air Corridors To Be Used for Flights in the Respective Zones of Occupation in Germany", dated Nov 22.
Interestingly, perhaps to make it look like some kind of parity was being achieved, there were six corridors proposed at this stage of the negotiations, but only four seems to have had any real relevance as the other two (to Warsaw and Prague) were between Soviet-controlled regions and Berlin:
; in detail the proposed corridors were Berlin–Hamburg,
Berlin–Hannover (Bückeburg), Berlin–Frankfurt on Main,
Berlin–Warsaw, Berlin–Prague, and Berlin–Copenhagen. These were supposed to be "each twenty English miles wide (ten miles on each side of the centre line of the corridor) which could be used by aircraft of the four Allied Nations with full freedom of action." (The "limited distribution" map that supposed had these pictured is not included in the US archives.)
It looks like the (enacted) BASC rules were agreed upon in a "Second Revision, dated 13 December 1945, to be transmitted to the Coordinating Committee" redacted by the Air Directorate Secretariat to the Allied Secretariat and signed off by lower level brass. For example Maj.-Gen. Harper who signs off on this for the US side doesn't even have a Wikipedia bio, and neither does his Soviet counterpart Lt. Gen. of Avn. T. F. Kutsevalov (spelled Kutzevalov in some contemporary English-language documents), although the latter does have a Russian Wikipedia bio. These are the same names who appear on the Nov 22 report.
The air corridors themselves in the "final form" were apparently not agreed upon until 31 December 1945, the date of the "Report of the Committee on Aviation of the Air Directorate" (control number "DAIR/P(45)71 Revise") on the matter of the "Flight Rules for Aircraft Flying in Air Corridors in Germany and Berlin Control Zone". These are also signed off by Harper and Kutzevalov. This document only mentions the 3 corridors that were actually enacted: "The following air corridors have been established: Frankfurt–Berlin, Bückeburg–Berlin, [and] Hamburg–Berlin.
Each of the above corridors is 20 English miles (32 kilometers) wide, i.e., 10 miles (16 kilometers) each side of the center line. It is probable that from time to time additional corridors may be established, and these rules apply equally to any such corridors." This Report also makes reference to BASC as having already been established in the Allied Control Authority Building (now Kammergericht).
I'm unsure if there was another top-level discussion e.g. involving Clay and Sokolovsky on the matter after that. It's possible the archives have that in a separate "compartment" since the year 1945 had ended...
There was certainly a "DAIR/P(45)71 Second Revise" referenced in much later documents e.g. telegrams from 1948. Apparently some changes were made (at least) to the night flight rules in 1946:
the meeting of October 22, 1946, of the Air Directorate of the Allied Control Authority at which agreement was reached on document DAIR/P(45)71 Second Revise regarding night rules in the Berlin air.
This revised document "DAIR/P(45)71 Second Revise" cannot be found on the web as far as I can tell, but some 1964 documents refer to it as still authoritative:
the Second Revise of DAIR/P(45)71, date October 22, 1946, still controls as to flight rules
That 1964 State Department Airgram ("cable") titled "Allied Right to Local Flights in the Berlin Control Zone" also mentions that the Soviets attempted to renegotiate the agreement on two occasions, in 1947 and '48 attempting to impose additional restrictions like (in 1947) limiting the purpose of the flights to "absolute necessity". However, since decisions in the Air Committee were taken by unanimity and the US objected to the proposed wording changes, nothing came of that.
A more extensive 1948 Soviet proposal, DOCS/P(48)7, attempted (among other things) to "categorically forbid [...] local flight in cloud cover of the Greater Berlin Zone". This proposal was actually never even discussed in the committees as the
Allied Council simply ceased to meet (at all levels) before this Soviet change/proposal could be even discussed, as the Soviets boycotted all Council meetings stating in March 1948 (although almost certainly the Western powers would have rejected the proposed change; there exists a March 22 US draft position statement to that effect.) Note that BASC itself continued to function, but it had no power to change the rules.
This 1964 document also has a 3-page summary of the changes to the rules that were made throughout 1946, i.e. while there wasn't complete deadlock. I'm not finding any of those particularly noteworthy to include here... There weren't any changes to corridors themselves, but various minutia regarding landing zones in Berlin (e.g. these were set to a 20-mile radius around pre-approved points), duty to report flights within certain time frames etc. The final bits of this bureaucratic history mention that
October 22, 1946: Aviation Committee submitted the revision to Air Directorate. DAIR/P(46)144.
October 25, 1946, Air Directorate approved the Committee paper as DAIR/P(45)71 Second Revise and decided to send it to
the Military Missions accredited with the Control
That 1964 cable but doesn't discuss any of the prior 1945 negotiations in any detail though. (In fact it states that the "First Revise" of DAIR/P(45)71 had been [temporarily] lost by the US side... although apparently it has been found again since then, as the State Department [amusingly] only has that version on the web, nowadays.)
Interestingly, perhaps, it seems that the US did not make public the exact text of the air corridors agreement until 1961, and that was in response to Soviet claims that the agreement had been "temporary". (The Eastern bloc started to build the Berlin wall that year.)