Exact power for normal location alternatives is obtained for the bivariate sign tests of Blumen  and Hodges . A recursive scheme, used in conjunction with a computer, permits comparison of the two tests for sample sizes $n = 8(1)12$. Efficiency values relative to Hotelling's bivariate $T^2$ test are also obtained for the test of Hodges. Slight power differences are noted for the sign tests along with surprisingly high power when compared with the $T^2$.
"Small Sample Power of the Bivariate Sign Tests of Blumen and Hodges." Ann. Math. Statist. 35 (4) 1576 - 1582, December, 1964. https://doi.org/10.1214/aoms/1177700382