J'ai un formulaire qui ressemble à ça :

<form action="<?php bloginfo('siteurl'); ?>" id="searchform" method="get">
     <fieldset>
         <label for="s" class="screen-reader-text">Recherche</label>
         <input class="search" id="s" name="s" placeholder="Recherche" required />
         <div class="text-center"><button type="submit" class="searchsubmit" alt="Recherche"><i class="icon-search"></i></button></div>
     </fieldset>
     <div class="text-center"><button type="reset" id="close" alt="close"><i class="icon-clear"></i></button></div>
</form>

Avec ce CSS :

input, button {
  text-decoration:none;
  background: transparent;
  border: none;
  -webkit-appearance: none;
  box-shadow: none;
}

button:active, button:focus, button:hover {
  text-decoration:none;
  background: transparent;
  border: none;
  -webkit-appearance: none;
  box-shadow: none;
}

#searchform {
  position: fixed;
  top: 3.2rem;
  left: 0;
  right: 0;
  bottom: 0;
  margin: 0;
  background: #FFF;
  opacity: 0;
  visibility: hidden;
  z-index: 1999;
  transform: scale(0);
  transition: all 400ms ease-in-out;
}
#searchform.active {
  opacity: 1;
  visibility: visible;
  transform: scale(1);
}
#searchform fieldset {
  position: absolute;
  top: 0;
  left: 0;
  right: 0;
  bottom: 0;
  width: 95%;
  height: 12rem;
  line-height: 8rem;
  margin: auto;
  border: none;

#searchform fieldset .search {
  width: 95%;
  padding: 0;
  border: 0;
  outline: 0;
  background: transparent;
  font-family: 'Noto Sans', sans-serif;
  font-size: 8rem;
  color: #000;
  border-bottom: 0.1rem solid #CCC;
}

#searchform fieldset .searchsubmit {
  cursor: pointer;
  font-size: 8rem;
  color: #000;
  margin-top: 6rem;
  transition: all 0.6s ease-in-out;
}
#searchform fieldset .searchsubmit:hover {
  color: #00C78C;
}


#searchform #close {
  cursor: pointer;
  font-size: 5rem;
  color: #000;
  margin-top: 4rem;
  transition: all 0.6s ease-in-out;
}
#searchform #close:hover {
  color: #00C78C;
}

et un JS qui rajoute la classe active pour ouvrir/fermer un overlay.

Quand je "clique" sur les boutons searchsubmit ou close sur un mobile ( android ) ça m'ouvre le clavier pendant une fraction de seconde.