Pain behind the knee comes and goes from one knee to the other help when i wear a light compression brace was in military for 4 years what could it be?

Possible ligament issues: If you've been in the military you were involved in a lot of physical activity. That's strain puts pressure on your knees from bending lifting moving side to side. If the brace helps continue to wear it. If you want to take it a step further make an appointment with an orthopedic to see if an MRI or physical therapy or more in depth diagnosis is indicated. Good luck!