adaptation of NIST sp800-22 for short sequences
You will simply not be testing those properties and thus structured nonrandom sequences may pass with respect to tested properties.

For a simplistic example random excursion test fails if the maximum magnitude of the cumulative sums defined by the -1,+1 version of the sequence is too large (much larger than say  $2 \sqrt{n}$ where $n$ is the sequence length.

So you can have long runs and fail random excursions but still pass other tests, e.g., the frequency test.

The paper https://arxiv.org/pdf/1208.5740.pdf has some intuitive discussion of what some of the tests are aimed at.