Consider an asymptotic sequence of sparse spiked covariance testing problems with $d\to\infty$, $n=n_d\to\infty$, $k=k_d\to\infty$, $k/d\to0$, and $\log \binom{d}{k}\to\infty$. Under $H_1$, take the spike $v$ from the uniform prior on $k$-sparse vectors with nonzero coordinates equal to $\pm k^{-1/2}$. There are constants $0<c<C<\infty$ such that the following hold for the sum of type I and average type II errors against this prior. If \begin{align*} \theta \ge C\sqrt{\frac{k\log(d/k)}{n}}, \end{align*} then the exhaustive sparse eigenvalue scan has error tending to $0$. If \begin{align*} \theta \le c\sqrt{\frac{k\log(d/k)}{n}} \end{align*} then the second moment of the uniform-sign sparse mixture likelihood ratio tends to $1$. Consequently, the null law and the prior-mixture alternative are mutually contiguous, so every test has limiting error bounded away from $0$.