When $K$ is finite or $p$-adic the answer to your question is negative. Indeed there exist maximal tori which are anisotropic. Those tori are not included in any parabolic subgroup, so they cannnot stabilize a non trivial totally isotropic subspace.

When $K$ is finite or $p$-adic the answer to your question is negative. Indeed there exist maximal tori which are anisotropic. Those tori are not included in any proper parabolic subgroup, so they cannnot stabilize a non trivial totally isotropic subspace.