Thanks for all the suggestions. In response to some of the questions:

I believe the steerer tube is carbon, not absolutely positive. Guess I'll have to take it apart to look.

I store it in the garage, so it is "inside" out of the rain, but not in heated or cooled space. Could be condensation I suppose.

The brown discharge is coming only from the upper end of the head tube, not the bottom end.

Yes, it is an integrated headset (FSA IS-2).

And yes, the question about if the fork is carbon and the frame is titanium, where would rust come from, is exactly what I was wondering. The only steel in there should be the bearings. Can't imagine they would produce enough rust for it to be running down my leg.