Following up on the ideas in @Nick's answer & comments, you can see how wide the bandwidth needs to be to *just* flatten out the secondary mode:

![enter image description here][1]

Take this kernel density estimate as the proximal null—the distribution closest to the data yet still consistent with the null hypothesis that it's a sample from a unimodal population— & simulate from it. In the simulated samples the secondary mode doesn't often look so distinct, & you needn't widen the bandwidth as much to flatten it out.

![`enter image description here`][2]


  [1]: https://i.sstatic.net/xg8ic.png
  [2]: https://i.sstatic.net/4sJ45.png

Formalizing this approach leads to the test given in Silverman (1981), "Using kernel density estimates to investigate modality", *JRSS B*, **43**, 1.