For our citizens who identify as neither female nor male, estimated to be six tenths of one percent of the population, they would qualify for either seat. It is hoped that the federal government would form a department to promote gender equality as many other countries have done.
The announcement on International Women's Day in 2021 of an executive order establishing a Gender Policy Council within the White House is a start.
Here is a brief summary.
The Congress proposes an amendment in the form of a joint resolution requiring a two-thirds majority vote in both the House of Representatives and the Senate.
At that point, the amendment process is launched and the amendment makes its journey through the states and back to the Federal level, as follows:
There are two Senators from each State, so one Senate seat would be for a woman and one would be for a man.
For the House of Representatives, there is a formula to allocate the seats.  This formula would be updated to shift slightly to have an even number of representatives from each State, based on population. Each State would send the same number of female representatives as male representatives.
 1/15/2015 http://www.archives.gov/federal-register/constitution/
 http://en.wikipedia.org/wiki/List_of_amendments_to_the_United_States_Constitution 2/8/15.
The original document goes to the National Archives and Records Administration’s Office of the Federal Register for processing and publication.
The proposed amendment is then submitted to the Governor of each State.
The Governors submit the amendment to their State legislatures, although in the past, some State legislatures have not waited to receive official notice before taking action on a proposed amendment.
Each State ratifies the proposed amendment and sends to the Archivist a certified copy of the State action, which is then sent to the Director of the Federal Register.
The Office of the Federal Register processes these documents and retains them until an amendment is adopted or fails and then sends the records to the National Archives for preservation.
A proposed amendment becomes part of the Constitution as soon as it is ratified by three-fourths of the States (38 of 50 States).
The last amendment to be adopted (27th Amendment which delays laws affecting Congressional salary from taking effect until after the next election of representatives) was certified on May 18, 1992.