I've been trying to do the maths but to be honest I'm struggling a bit.

I have the Schwarzchild radius of a 2.6 solar mass BH at 4km, and estimating the radius of the K-star at about 500,000km

So I'm trying to calculate the deflection angles for 2.6 solar masses at those distances from a point mass to get the maximum deflection angle at the event horizon and the minimum deflection angle for light at the K-star radius from that point mass.

angle = 4GM/c

^{2}b where b is the distance of the passing light from the point mass

That's where I'm losing my thread with the calculations.

If you can work out the angles you'll be able to use trig to find a minimum and maximum focal length.

I'm convinced that the planet at ~1M km from the black hole is in between and would get a distinct ring effect during the eclipse resulting in a massive spike in EM radiation, which even for a short period of time would have a significant impact.