JSFiddle - React, Tailwind, and code Playground

HTML

<input type="text" id="mail_rem" value="test" />
<input type="button" id="rem_but" value="Click Me" />

<input type="button" id="rem_but2" value="Click to Enable" />

JavaScript

$(document).ready(function() {
 $("#rem_but").click(function() {

 var mail_name = $.trim($("#mail_rem").val());
 var dataString = 'mail_name='+ mail_name;
 
 if (mail_name === "") {  
    $(this).prop("disabled", true); }
 else {  
    $(this).prop("disabled", false); }
 });
    
    $("#rem_but2").click(function() {
      $("#rem_but").prop("disabled", false);
    });
    
    $("#mail_rem").keyup(function() {
        var currentVal = $.trim($(this).val());
       
        if (currentVal === "") {
          $("#rem_but").prop("disabled", true)
              } else {
                  $("#rem_but").prop("disabled", false)
              }
    });
});