  A sign pattern is an array with entries in $\{+,-,0\}$. A matrix $Q$ is row
orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced
in [B.A.~Curtis and B.L.~Shader, Sign patterns of orthogonal matrices and the
strong inner product property, Linear Algebra Appl. 592: 228--259, 2020], is an
important tool when determining whether a sign pattern allows row orthogonality
because it guarantees there is a nearby matrix with the same property, allowing
zero entries to be perturbed to nonzero entries, while preserving the sign of
every nonzero entry. This paper uses the SIPP to initiate the study of
conditions under which random sign patterns allow row orthogonality with high
probability. Building on prior work, $5\times n$ nowhere zero sign patterns
that minimally allow orthogonality are determined. Conditions on zero entries
in a sign pattern are established that guarantee any row orthogonal matrix with
such a sign pattern has the SIPP.
