Fischer indole synthesis: significance of choice of acid catalyst
I'd like to take this opportunity to give a nutshell review of the Fischer indole synthesis for benifit of future readers. This highly useful synthetic tool, which was named after the famous chemist, Emil Fischer who discovered it in 1883 (Ref.1 &amp; 2)), is considered to be one of the best methods for preparing indoles. Hence, needless to say, it is the most widely used and versatile method for indole synthesis. The method simply converts converts ayrlhydrazones ($\bf{1}$) of an aldehyde or a ketone into corresponding indole ($\bf{8}$) in the presence of an acid catalyst (Ref.3 &amp; 4). The overall reaction is depicted in the top box in following image:

The proposed mechanism of The Fischer indole synthesis is also included for the convenience. As indicated, ayrlhydrazones ($\bf{1}$) are formed from a condensation reaction between an arylhydrazine and an aldehyde or ketone (reference to 2,4-dinitrophenylhydrazine test for aldehydes and ketones). In the presence of acid (Brønsted or Lewis), imine $\bf{1}$ is in equilibrium with $\bf{2}$ (protonated imine), $\bf{3}$ (enamine form), and $\bf{4}$ (protonated inamine). Once formed, $\bf{4}$ undergoes [3,3] sigmatropic rearrangement (ene-reaction; could visualize as azo-Cope rearrangement), forming a new $\ce{C-C}$ bond to give $\bf{5}$ (this is a key step of the mechanism). Imine $\bf{5}$ gains back aromaticity to form $\bf{6}$, which is the most stable isomer between two. The anilinic $\ce{NH2}$ of $\bf{6}$ attacks electron deficient imine group in the side chain ($\ce{C}$ of $\ce{CNH2+}$ group) intramolecularly to give the corresponding dihydroindole derivative, $\bf{7}$ (which is also another key step), which eventually release $\ce{NH4+}$, $\ce{NH3 + H+ &lt;=&gt; NH4+}$, to give stable indole derivative,  $\bf{8}$. Reference 3 has given excellent review on the mechanism and hence, for benefit of interested reader, the PDF has been attached.
The key feature to produce corresponding indole is need of a $\ce{CH2}$ group as noted (as indicated by a green circle; $\alpha$ to the original ketone or aldehyde). If this $\alpha$-$\ce{C}$ is $2^\circ$, then $\bf{7}$ would still release $\ce{NH3}$ to give corresponding cyclic imine derivative (Ref.5). For example, compound $\bf{10}$ was formed ( Ref.5) when $2^\circ$ $\alpha$-$\ce{C}$ is attacked selectively at $\bf{3}$ to $\bf{4}$ conversion (thermodynamically stable enamine):

However, except for the situation to make $\bf{10}$, and the intention is making indole derivative of interest, the stereo selectivity at sigma-tropic rearrangement to give $\bf{5}$ and thereafter would not matter since at the end, all of stereocenters involved would be diminished (see the scheme above). Therefore, the choice of acid to get selectivity in general synthesis of indoles is not as important as it was told elsewhere. In reality, a variety of catalysts (Table I in Ref.3) have been used to effect the indolization of arylhydrazones. According to the Ref.3 (an excellent review of the Fischer indole synthesis):

Generally speaking, it may be said that acids and many compounds capable of complex formation with organic ligands may act as catalysts.

In addition to the variety of catalysts listed in Table I of Ref.3, there are wide variety of other acid catalysts including organic acids such as tartaric acid (e.g., Ref.5) and p-toluenesulfonic acid (e.g., Ref.6). The bottom line is the indole formation by this method is independent of acid catalysis (e.g., Ref.7), although it is markedly accelerated by it.
It is also worth noting that this reaction has proven very useful for the pharmaceutical synthesis of antimigrane drugs (e.g., Ref.8 &amp; 9).

References:

Emil Fischer, Friedrich Jourdan, &quot;Ueber die Hydrazine der Brenztraubensäure,&quot; Berichte der deutschen chemischen Gesellschaft 1883, 16(2), 2241-2245 (https://doi.org/10.1002/cber.188301602141).
Emil Fischer,  Otto Hess, &quot;Synthese von Indolderivaten,&quot; Berichte der deutschen chemischen Gesellschaft 1884, 17(1), 559-568 (https://doi.org/10.1002/cber.188401701155).
B. Robinson, “The Fischer Indole Synthesis,” Chem. Rev. 1963, 63(4), 373–401 (https://doi.org/10.1021/cr60224a003)(PDF).
B. Robinson, “Studies on the Fischer indole synthesis,” Chem. Rev. 1969, 69(2), 227–250 (https://doi.org/10.1021/cr60258a004).
Sangram Gore, Sundarababu Baskaran, Burkhard König, “Fischer Indole Synthesis in Low Melting Mixtures,” Org. Lett. 2012, 14(17), 4568–4571 (https://doi.org/10.1021/ol302034r).
Seble Wagaw, Bryant H. Yang, Stephen L. Buchwald, &quot;A Palladium-Catalyzed Strategy for the Preparation of Indoles:  A Novel Entry into the Fischer Indole Synthesis,&quot; J. Am. Chem. Soc. 1998, 120(26), 6621-6622 (https://doi.org/10.1021/ja981045r).
Okiko Miyata, Yasuo Kimura, Kanami Muroya, Hajime Hiramatsu, Takeaki Naito, &quot;Thermal cyclization of N-trifluoroacetyl enehydrazines under mild conditions: A novel entry into the fischer indole synthesis,&quot; Tetrahedron Lett. 1999, 40(18), 3601-3604 (https://doi.org/10.1016/S0040-4039(99)00583-3).
Paul R. Brodfuehrer, Bang-Chi Chen, Thomas R. Sattelberg, Patrick R. Smith, Jayachandra P. Reddy, Derron R. Stark, Sandra L. Quinlan, J. Gregory Reid, John K. Thottathil, Shaopeng Wang, “An Efficient Fischer Indole Synthesis of Avitriptan, a Potent 5-HT$_\mathrm{1D}$ Receptor Agonist,” J. Org. Chem. 1997, 62(26), 9192–9202 (https://doi.org/10.1021/jo971368q).
Majid M. Heravi, Sahar Rohani, Vahideh Zadsirjan, Nazli Zahedi, “Fischer indole synthesis applied to the total synthesis of natural products,” RSC Adv. 2017, 7, 52852-52887 (DOI: 10.1039/C7RA10716A).