The question in volves differences in left and right sigma affecting the TJ result.
The answer: it can get ugly. For electrical systems, when they differ widely, look deeper, something is probably wrong with the transmitter or you need to fit farther and farther down the tails.
For optical systems it's more complicated and you see left-right asymmetries more often.
My prejudice, especially since I don't have to pay for test equipment, is to do the full measurement with a BERT and see what's really going on. If there really are asymmetries, you'll have check the accuracy of your dual-Dirac estimate with the BERT measurement.