Although this is kinda opinion based, I like the question about what's a good approach to place an easter egg into a website. Don't be too serious about it :-)
Generate the button completely with JS like:
document.easterEggBtn = function() {
button = $('<div/>');
button.addClass('secretButton');
button.on('click', 'easterEggFunction');
// Add more attributes
$('#buttonOuter').append(button);
}
Then use an online javascript obfuscator, and put that obfuscated code into your website.
Won't hide from any DOM inspector of course, but if someone only looks into the sourecode, he won't spot it right away.
Another way is to fake 'secret buttons': Put many hidden buttons into the code, so the visitor gets confused and doesn't know which of the 50 buttons is the real easter egg.