[Overread]

For me the end of the Tawny man series (I think) is where the fool explains that he would never force Fitz to love him (in the physical sense) because he is aware of Fitz's stance on single sex relationships.
Now this could go two ways; either this is the fools admission to being male, and thus the Amber line was a red herring (there are so many stories of women dressing up and acting as men, so maybe the fool does the total opposite).
Or it could be like Wyvern says, some sort of gender swapping evolution through time, or maybe there gender changes at their request - the fool started as a male, not expecting to fall in love with Fitz, when he did so as a male he (or it) realised that he could never change to be a women for Fitz as that would alienate Fitz from him - so he settled for the friendship with fitz. This allows the fool to change to be a women in the liveship series, and then accounts for a male shift back, when he returns to Fitz in Tawny man series (also - - come on people its called the Tawny MAN series - - - that could be a hint!)
for me I stick with option 1