Update:
Further (QC) testing in the Aviatik initially provided the same results. Turned on labels to verify range to target and took screenshots. At <200 yards the gunner tracked, but would not fire at, the enemy aircraft. Took a succession of screenshots to verify I was flying straight and level, no jinking. Switched seats as Pol suggested and scored several hits myself, confirming the gunner was still alive. But when I returned to the pilot's seat, nada...as in he fired nada dad-gummed shot.

While resizing the screenies so as not to overwhelm the board I noticed something...the EA were within the arc of the propeller. So I fired up the game again to remove that variable. This time, with the EA securely outside the propeller disc my man lost his inhibition and fired like his life depended on it. It seems he's coded no to shoot into his own prop and I was staying too nose-on the targets. Kudos to the team. Haven't tried to replicate the results in a campaign mission but I expect them to be the same.

While I'm here though, one other question arose from my testing. Can the Aviatik's port gun not be slid significantly into the forward quarter of the aircraft? I ran a final flight against two BE2's. The first I engaged to starboard and the gunner fired from roughly just outside the prop disc all the way back to the wing, or nearly. When I engaged the second EA to the port side I had to bring the target back to maybe 9:30 before he'd open up. Both mounting rails go well forward of the gunner's seat and it seems rather silly to be able to cover only the back left and front right (sitting in the gunner's seat, the starboard side gun stops at about the wing although I did not test the starboard gun's rearward firing arc against a target). I'm still on 1.26, so if this has been corrected in 2.0 I apologize.