Accurate spectral data of H(32)SOH and H(34)SOH at 1.3 THz were recorded using a synthesizer based multiplier spectrometer. The spectra were analyzed together with data from an earlier study which contain measurements at 1.9 THz. The combination of both data sets allows to determine experimentally the tunneling splitting of energy levels with K(a) = 4 and 5 for the first time. The obtained results are essential to test a novel model on torsional tunneling splitting in HSOH. Transitions with K(a) = 1 <-- 0, K(a) = 2 <-- 1, and K(a) = 3 <-- 2 all exhibit strong c-type and somewhat weaker b-type transitions. In contrary, transitions with K(a) = 4 <-- 3 display only c-type but no b-type transitions. The absence of b-type transitions is completely unexpected and yet not well understood. For the H(34)SOH isotopolog the data set has been substantially extended by the new measurements of (r)Q(3)-branch transitions at 1.3 THz. Based on the new data the accuracy of the H(34)SOH molecular parameters has been significantly improved.