Ng's conjecture for the second ratio moment at the zeros of the zeta function

Let the non-trivial zeros of the Riemann zeta function be written as $\rho=\tfrac12+i\gamma$. Assume the Riemann Hypothesis and that these zeros are simple. Ng's conjecture. As $T\to\infty$,

$$\sum_{0<\gamma\le T}\left|\frac{\zeta(2\rho)}{\zeta'(\rho)}\right|^2\sim\frac{T}{2\pi}.$$

This companion conjecture is attributed to Ng and remains open; the paper proves a lower bound of half the expected main term.