The Gemini spacecraft had two windows, one in each hatch in front of each astronaut. This artifact is the inner frame and gasket for the right-hand window. The right-hand seat on Gemini XII was occupied by Edwin E. "Buzz" Aldrin Jr. He flew with James Lovell as mission command pilot on a four day mission in November 1966, the last in the Gemini series. That mission proved the feasibility of doing work on a zero-G EVA ("spacewalk") and rendezvoused and docked with an Agena target vehicle.
This window frame was shipped separately from the spacecraft when NASA transferred the latter to the Smithsonian in 1968.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.