The Mars Curiosity rover carries a diverse instrument payload to characterize habitable environments in the sedimentary layers of Aeolis Mons. One of these instruments is Sample Analysis at Mars (SAM), which contains a mass spectrometer that is capable of detecting organic compounds via pyrolysis gas chromatography mass spectrometry (py-GC-MS). To identify polar organic molecules, the SAM instrument carries the thermochemolysis reagent tetramethylammonium hydroxide (TMAH) in methanol (hereafter referred to as TMAH). TMAH can liberate fatty acids bound in macromolecules or chemically bound monomers associated with mineral phases and make these organics detectable via gas chromatography mass spectrometry (GC-MS) by methylation. Fatty acids, a type of carboxylic acid that contains a carboxyl functional group, are of particular interest given their presence in both biotic and abiotic materials. This work represents the first analyses of a suite of Mars-analog samples using the TMAH experiment under select SAM-like conditions. Samples analyzed include iron oxyhydroxides and iron oxyhydroxysulfates, a mixture of iron oxides/oxyhydroxides and clays, iron sulfide, siliceous sinter, carbonates, and shale. The TMAH experiments produced detectable signals under SAM-like pyrolysis conditions when organics were present either at high concentrations or in geologically modern systems. Although only a few analog samples exhibited a high abundance and variety of fatty acid methyl esters (FAMEs), FAMEs were detected in the majority of analog samples tested. When utilized, the TMAH thermochemolysis experiment on SAM could be an opportunity to detect organic molecules bound in macromolecules on Mars. The detection of a FAME profile is of great astrobiological interest, as it could provide information regarding the source of martian organic material detected by SAM.