Asymptotic equipartition of twin Ramanujan-prime pairs

Let $\pi_2(x)$ count twin-prime pairs up to $x$, and let $\pi_{2,1}(x)$ and $\pi_{2,2}(x)$ count, respectively, twin-prime pairs with one and with two Ramanujan primes.

Twin Ramanujan-prime asymptotic conjecture. If $\pi_2(x)\to\infty$ as $x\to\infty$, then

$$\pi_{2,1}(x)\sim\pi_{2,2}(x)\sim\frac12\pi_2(x).$$

The conjecture formalizes the preceding heuristic that the two types of twin-prime pairs should occur in asymptotically equal proportions. The supplied text gives no resolution.