For a group $G$ with a non-elementary general type action by isometries on a Gromov hyperbolic geodesic space $(X,d)$, it is well known that you can construct free subgroups of $G$ via the ping pong argument with (sufficiently large powers of) two hyperbolic elements with distinct fixed points in $\partial X$.

In this question I ask for a reference for the case of ping pong with two parabolic isometries. This is perhaps well known in the case of $X=\mathbb{H}^2$, but I am interested in general Gromov hyperbolic spaces. I think the following should be true, but ideally I would like to cite it. Does anyone know of such a reference?

Let $G$ be a group acting by isometries (not necessarily properly) on a Gromov hyperbolic geodesic metric space $(X,d)$. Fix a basepoint $o\in X$.

Suppose

- that $f,g\in G$ both induce parabolic isometries on $(X,d)$,
- the fixed points of $f$ and $g$ in $\partial X$ are distinct, and
- for any $B>0$ there exists $N>0$ such that for all $n>N$ we have $d(o,f^n o),d(o,g^n o) >B$.

Then for sufficiently large $M$ we have that $f^M$ and $g^M$ generate a free group $F$ of rank two, and, any non-trivial $h\in F$ is either hyperbolic on $(X,d)$ or $h$ is conjugate (in $F$) to a power of $f$ or $g$.

A reference would be ideal and greatly appreciated. Thank you.