JSFiddle - React, Tailwind, and code Playground

HTML

<select data-bind="value: test, visible: showDropdown">
    <option></option>
    <option>Option 1</option>
    <option>Option 2</option>
</select>
<button data-bind="text: test, visible: !showDropdown(), click: function() { showDropdown(true); }"></button>

JavaScript

var ViewModel = function() {
    var self = this;
    self.test = ko.observable('');
    self.showDropdown = ko.observable(true);
    self.test.subscribe(function(value) {
        if(value.length) {
            self.showDropdown(false);
        } else {
            self.showDropdown(true);
        }
    });
};
ko.applyBindings(ViewModel);