Define Sass variables with BEM using map.

bem-vars.scss

$searchbox: (
  input: (
    fg: black,
    bg: white,
    border: lighten(black, 25%);
    --focus: (
      border: cyan,
    )
  );

  button: (
    fg: white,
    bg: grayscale(mix(cyan, white, 60%)),
    --hover: (
      bg: cyan
    )
  )
);

.searchbox {
  input {
    $input: map-get($searchbox, input);

    border: 1px solid map-get($input, border);
    color: map-get($input, fg);
    background-color: map-get($input, bg);

    &:focus {
      $input--focus: map-get($input, --focus);

      border-color: map-get($input--focus, border);
    }
  }
}