Catalyzes the formation of an amide bond between tyramine and the gamma carboxy group of L-glutamate. The enzyme also accepts phenylethylamine in vitro. ATP + L-glutamate + tyramine = ADP + gamma-L-glutamyltyramine + H(+) + phosphate Binds 2 magnesium or manganese ions per subunit. kcat is 4.8 sec(-1) toward tyramine. kcat is 5.8 sec(-1) toward L-glutamate. kcat is 5.9 sec(-1) toward ATP. Optimum pH is 6.7. Cofactor biosynthesis; methanofuran biosynthesis.