Conjectures for two-cycles with arbitrary and primitive-root conditions

Let $p$ be prime. For conditions on $g$ and $h$, let $T_{g\,\mathrm{condition},h\,\mathrm{condition}}(p)$ denote the number of corresponding two-cycle solutions modulo $p$, where $\mathop\mathsf{PR}$ means primitive root, $\mathop\mathsf{ANY}$ means unrestricted, and $\bullet$ denotes any one of the four conditions used on $h$.

Two-cycle counting conjectures. The paper conjectures

$$T_{g\,\mathop\mathsf{PR},h\,\mathop\mathsf{ANY}}(p)\approx 2\phi(p-1),\qquad T_{g\,\mathop\mathsf{ANY},h\,\mathop\mathsf{ANY}}(p)\approx 2(p-1).$$

It further conjectures

$$T_{g\,\mathop\mathsf{RP},h\,\bullet}(p)\approx \left[\frac{\phi(p-1)}{p-1}\right]T_{g\,\mathop\mathsf{ANY},h\,\bullet}(p),$$ $$T_{g\,\mathop\mathsf{RPPR},h\,\bullet}(p)\approx \left[\frac{\phi(p-1)}{p-1}\right]T_{g\,\mathop\mathsf{PR},h\,\bullet}(p).$$

These heuristic formulas concern the predicted numbers of solutions to the discrete-logarithm two-cycle equations under various primitive-root restrictions. The source presents them as conjectural birthday-paradox estimates; no resolution is supplied.