Yes, a little-documented one. As Kyle says, from the 1950s. The writers of the thesis from which Maurice's quote comes seem to have got rather confused about the chronology - indeed, Avondale had not even opened for business in 1935. LT 1938 was actually delivered 12/1952 (Avondale, Yard 397). Now a training ship for the Ecuadorian Coastguard, which is part of the Navy, she was previously operated by Astilleros Navales Ecuatorianos (Astinave) at Guayaquil - effectively another organ of the Navy.

Presumably now based at the Navy College at Salinas.

Hello,

Here some infos about this vessel.
Regards
Maurice

“El B.A.E. Marañón (BESMAR) ex U.S ARMY LT 1938 fue construido en
el año 1935 por la compañía AVONDALE MARINE WAYS. INC. En New
Orleans, entró en servicio del ejército de los Estados Unidos en el año 1938
y fue incorporado a la Armada del Ecuador como REMOLCADOR SANGAY,
ofreciendo su servicio en ASTINAVE, En el año 2002 fue entregado a la
Escuela Naval como buque de Instrucción para Guardiamarinas (Figura 1.1).
Finalmente en el año 2011 cambia su nombre a B.A.E Marañón, en
remembranza a aquel primer Buque Escuela del año 1905 donde funcionó la
primera Escuela Náutica y se formaron los primeros Guardiamarinas.”

Looks like one of the former 107-ft US Army LT-type tugs built in the 1950's. Unfortunately, the Army has kept very poor records regarding the fates of its vessels, so I can't really say much more about which it may be.
Kind Regards,
Kyle

Not listed in the 2012-2013 edition of Jane's Fighting Ships. Name is on funnel. Looks like MARANON.