If I remember correctly, this used to drop from Hyena, open world bosses in WONY. Even though exotics have been added to the open world loot pool I have found that farming them how they originally dropped is more successful.
I recommend doing targeted loot SMG. I finally got mine two days ago when SMGs were targeted loot in Civic Center. As reward for an open world activity. And directly afterwards, I got a second one in the exotic cache for the Global Event. Typically RNG in TD2. Good luck!
Find somebody that has better RNG. I have close to 100 raid completions and never got an Eagle bearer drop. Also never got a lady death drop, but my lucky rabbits feet have gotten plenty.
I got 3 yesterday.One from weekly shd requesition (exotic cache), 1 from an elite convoy near the crash site CP and another one from a CP3 where smg are targeted.