AFAIK there doesn’t seem to be a correlation between certain fragments of files being more rare than other fragments. I’ve completed this file on almost all of my alts and luck doesn’t appear to influence what fragments you get. As such you can definitely get a run of bad “luck” and have the fragment you need take a long time to drop.

However, that being said more random files appears to be one of the commonly dropped fragments for second wife at least. Perhaps you should do 4x Second Wife until you get this file complete unless you are absolute committed to the flezz raising strategy.