The source of the material I'm providing is the book
Railways of Peru: Voume 1 - The Norther Lines by Robert D. Whetham, published by Trackside Publications of Skipton, North Yorkshire, England in 2007.
At least in the northern part of Peru it seems that most of the rail lines were less than standard gauge - 914mm (3'), 600mm (24"), etc. -- but there were some standard gauge lines. The lines were isolated with most lines running inland from port facilities. These lines served either agricultural or mineral industries. The common carriers seem to often start with local investors, taken over by the national government, and then turned over to international investors as part of paying off national debt.
The Hacienda Casa Grande operation connected with the FC de Trujillo a common carrier 3' gauge operation. The Trujillo ran to Trujillo and then to the port of Salverry. This line was first autherized to a private investor in 1869, but started by the government in 1872 and almost completed in 1879 when the War of the Pacific broke out. The line suffered during this war between Chile and Peru. The line was turned over to the Peruvian Corporation in 1890 as part of the restructuring of the national debt. Baldwin supplied locomotives in the 1870s-90s most of them would not be out of place on USA lines (one of these even made its way back to the United States for restoration and display); then Alco supplied locomotives in the 20th century. This line operated until 1967.
The railroad of Hacienda Casa Grande itself connected with the port of Chicama. This operation seems to have started in 1898 and was both 914mm (3' gauge) and 1067mm (42" gauge). In 1920 the 3' gauge line was constructed to Chicama. The Alco 2-8-2 locomotives came at that time; before that there only appears to have more typical plantation locomotives. The three Army 2-8-2s came after WWII after service on the White Pass. There were also second hand 2-8-0s from the Trujillo and Hacienda Roma. The railway closed in 1970 except for an operation at the pier at Puerto Chicama that used a Plymouth diesel-mechanical.
The map below is copied from the book. It shows other plantation railways that connected with the Trujillo -- Hacienda Laredo, Hacienda Cartavio, Hacienda Pampas, Hacienda Roma, Hacienda Chicamita, Hacienda Chiquitoy (later part of Casa Grande), Hacineda Chiclin, Hacienda Zauzal. All of these were 914mm (3' gauge) most operated small 4-wheel planation locomotives, but the Roma had 2-8-0s and the Cartavio had a 2-truck Shay (operating until the mid-60s).
The 96-page book is available from English book sellers like Motor Books and Ian Allan for ₤20.95 (Pounds) softbound. Volume 2 about the southern lines has been out about a month or so -- I have yet to receive my copy.
I hope this helps.
Brian Norden