One way of doing it is to not make the idle animation "looping" but using instead the "repeat" option (in the animation editor properties)
Like repeat 10 times.
And then simply use -> on finished "idle" animation -> play "blink" -> on finished "blink" -> play idle.
But if you want to add more randomness, using a timer system when idle will give you more control over it.
Using wait action like you did will confuse the engine as it will remember that it is waiting for something (and it will trigger each time you stop, stacking all the previous wait action on top of each other), so if you start walking after being idle, the engine will still run the idle wait action even though you are moving.