Jimmi...
I've never tried singing to a deer before.
Any time you go to the woods where deer are, always take a white handkerchief with you.
I always carry one in my back pocket. If I'm spotted by a deer like you were.. I will squat down and pull the handkerchief from my pocket and let it unfold, hold it in front of me and wiggle it back and forth a few times.
This tells the deer.. "I'm another deer, everything is cool."
I've had deer walk almost on top of me before they discovered I wasn't one of them!
If you'll notice most of the time they will wiggle their tail before dropping their head to eat...
this is an all clear sign to others. This works mostly with does or young bucks... older bucks are harder to fool!