See link to video to hear noise:
I hear this noise once I start my FD and it doesn't go away no matter if I engage a gear, push the clutch pedal in, rev, or drive. I can't pinpoint where it's coming from. Any help would be appreciated.

Stock 1993 Rx7 FD

 

I had a similar problem on my FC and it turned out to be the air pump vane.. . .I put my hand on the air pump housing and sure enough the vibration I felt coincided with the noise.

I assume the noise changes with the RPM?. . .Just food for thought.

 

I actually just swapped out my old air pump for a used one, I will do the hand on pump test as you suggested but it really sounds more to the rear of the engine(flywheel/starter area). The sound does doesn't sound louder when you increase RPM but the noise sounds quicker like something spinning.

 

pull off the belts and start it up. that'll tell you if its internal or not