A Theorem by Gallo, Goldman and Porter states the following:

Let $S_g$ be a closed orientable surface of genus $g$ with fundamental group $\Gamma_g$, and fix a non-elementary representation $\rho\colon \Gamma_g \to PSL(2,\mathbb{R})$. Then, there exists a pants decomposition of $S_g$ whose curves are all taken by $\rho$ into hyperbolic elements.

I am looking for a reference to a proof of this statement. I know that the above result is a corollary to the results proved in Sections 3-4-5 of

Gallo, Kapovich, Marden, "The monodromy groups of Schwarzian equations on closed Riemann surfaces", Ann. of Math. (2) 151 (2000), no. 2, 625–704.

However, that paper deals with the more general case of representations into $PSL(2,\mathbb{C})$, so I expect that the proof in the real case could be shorter.

As stated by Tan in "Branched CP1-structures on surfaces with prescribed real holonomy", Math. Ann. 300 (1994), no. 4, 649–667,

there is a proof of the theorem above result in

D.M. Gallo, W.M. Goldman, R.M. Porter, "Projective structures with monodromy in PSL(2,R)", preprint.

However, I am not able to find this preprint. When looking for that preprint, MathSciNet redirects to the paper

Goldman, "Projective structures with Fuchsian holonomy", J. Differential Geom. 25 (1987), no. 3, 297–326,

but I am not sure that the statement I am interested in is proved there.