My headphones work, my speaker works, my radio works. When i plug in my headset its shuts off the speaker but nothing comes through the headset. Sorry you're confused.
So if I am understanding you correctly, your headphones work on another piece of equipment so we know they are good. The speaker works on the FT-1000 so we know it is good.
So the audio is getting from the amp to the speaker and is being cut off when you plug in the headphones, but you don't hear anything in the headphones. Do your headphones have a mono plug or stereo plug? Is it a 1/4" mono plug or are you using a mini stereo plug through an adapter? It sounds to me like a plug issue.