In this guide you can read info about how to find all 3 of the menu easter eggs as of 1.4 Update. Found exclusively by myself after 10 minutes of clicking every nook and cranny on the menu.
All the Eggs
Here's a completed picture with all three easter eggs found:
First you must click the E on the word STARDEW, you have to do this multiple times until the Alien appears. You will know you're doing it right when you hear knocking. Make sure to do the top E not the bottom one.
In order to get the junimos you must click the leaves on the sign. Once you click them smaller pedals will fall down, once you click it a sufficient amount of times the junimos appear. You can unlike the other easter eggs click the leaves to get the pedal effect as much as you want.
For this one you have to click on the Right bottom nail on the W of Stardew. You click it multiple times until you see butterflies appear around the banner.
This took me maybe about 10 minutes of goobering about to find this. It's such a small detail I never would have guessed. I stumbled upon it on the first time I clicked the nail and heard the tapping noise.