I am wondering if there is a general rule as to which direction any burn in would be heading
Seems to me to be pretty logical that the answer would be no. Obviously it would be dependent on the type of component (amp, cd player, preamp, speaker, interconnect cable, speaker cable, etc. etc.); and on the technology used (tube, solid state, dynamic speaker, electrostatic speaker, cone driver, dome driver, ribbon driver, electrostatic membrane, etc. etc.); the specific design of the particular example of the component type and technology, etc., etc.
I agree with Shadorne's comments as well.
Regards,
-- Al