Drawing border colors during a CSS transition

Question

button {
  background: none;
  border: 0;
  box-sizing: border-box;
  margin: 1em;
  padding: 1em 2em;
  box-shadow: inset 0 0 0 2px #f45e61;
  color: #f45e61;
  font-size: inherit;
  font-weight: 700;
  position: relative;
  vertical-align: middle;
}
button::before, button::after {
  box-sizing: inherit;
  content: " ";
  position: absolute;
  width: 100%;
  height: 100%;
}
.draw {
  transition: color 0.25s;
}
.draw::before, .draw::after {
  border: 2px solid transparent;
  width: 0;
  height: 0;
  transition: width 1.25s ease-out 1.25s, height 1.25s ease-out 1.25s;

}
.draw::before {
  top: 0;
  left: 0;
}
.draw::after {
  bottom: 0;
  right: 0;
}
.draw:hover {
  color: #60daaa;
}
.draw:hover::before, .draw:hover::after {
  width: 100%;
  height: 100%;
}
.draw:hover::before {
  border-top-color: #60daaa;
  border-right-color: #60daaa;
  transition: width 0.25s ease-out, height 0.25s ease-out 0.25s;
}
.draw:hover::after {
  border-bottom-color: #60daaa;
  border-left-color: #60daaa;
  transition: border-color 0s ease-out 0.5s, width 0.25s ease-out 0.5s, height 0.25s ease-out 0.75s;
}

<section class="buttons">
  <button class="draw">Draw</button>
</section>

Answer 1

I would use multiple linear-gradient and a complex animation (by animating size/position of each one) to obtain the final result. If you get the trick you can easily adjust the different values to obtain any animation you want.

.draw {
  padding: 20px 50px;
  outline:none;
  border: none;
  box-shadow: none;
  background-image: 
  linear-gradient(#f45e61, #f45e61), 
  linear-gradient(#f45e61, #f45e61), 
  linear-gradient(#f45e61, #f45e61), 
  linear-gradient(#f45e61, #f45e61), 
  
  linear-gradient(#60daaa, #60daaa), 
  linear-gradient(#60daaa, #60daaa), 
  linear-gradient(#60daaa, #60daaa), 
  linear-gradient(#60daaa, #60daaa);
  
  background-position: 0 0, 0 0, 0 100%, 0 100%, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 0%, 0% 3px, 0% 3px, 3px 0%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;
  background-color:transparent;
  background-repeat:no-repeat;
  transition:0.2s linear;
}

.draw:hover {
  background-position: 0 100%, 0 0, 0 100%, 100% 0, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 0%, 100% 3px, 0% 3px,3px 0%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;
  animation: animate 1.4s linear infinite 0.2s;
}

@keyframes animate {
  0% {
  background-position: 0 100%, 0 0, 0 100%, 100% 0, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 0%, 100% 3px, 0% 3px,3px 0%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;
  }
  40% {
  background-position: 0 100%, 100% 0, 100% 100%, 100% 0, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 0%, 100% 3px, 0% 3px,3px 100%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;
  }
  60% {
  background-position: 0 100%, 100% 0, 100% 100%, 100% 100%, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 0%, 0% 3px, 100% 3px,3px 100%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;
  }
  70% {
  background-position: 0 100%, 100% 0, 0% 100%, 100% 100%, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 100%, 0% 3px, 100% 3px,3px 0%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;
  }
  80% {
  background-position: 0% 0%, 0% 0, 0% 100%, 100% 100%, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 100%, 0% 3px, 0% 3px,3px 0%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;
  }
  100% {
  background-position: 0% 0%, 0 0, 0 100%, 100% 100%, 
                       0 0, 0 0, 0 100%, 100% 0;
  background-size: 3px 0%, 100% 3px, 0% 3px,3px 0%,  
                   3px 100%, 100% 3px, 100% 3px,3px 100%;  
  }
}

<button class="draw">Draw</button>