Movement is the last thing you want…
Whether pulsating or rotating, all visual changes in the interface risk attracting the user's attention—and you've said they're supposed to be doing something else for the duration of this wait time. Why distract users by showing visual movement?
Before the user clicks the button, show no wait feedback.
After the user clicks the button, if the wait time has elapsed, proceed. The user doesn't need to know that there was a wait time.,
After the user clicks the button, if there is more then 0.4 seconds of remaining wait time, show the wait feedback then. The amount of wait time is a known quantity, so ensure the feedback shows that the wait time is finite—in the style of a progress-bar.
Here's a suggestion—but there are many other possible solutions. To signal that the wait is directly involved in delaying the button's action, combine the button and the progress-bar feedback: