Thiol S-methyltransferase that catalyzes the transfer of a methyl group from S-adenosyl-L-methionine to alkyl and phenolic thiol-containing acceptor substrates. Together with TMT1B accounts for most of S-thiol methylation activity in the endoplasmic reticulum of hepatocytes. Selectively methylates S-centered nucleophiles from metabolites such as hydrogen sulfide and dithiothreitol.