Ever wonder what is the best time of day to shoot a double exposure? Usually it's the "golden hour" (the hour right before sunset) but this is not always the case with a double exposure photograph. One of the keys to shooting a great double exposure is to "silhouette" the subject. In order to do that you'll need the background (the sky) to be filled with a lot of even light and even color. If there are a ton of clouds that are covering 100% of the sky then it really doesn't matter what time you shoot because the sky will have a nice, soft, even look to it when blowing out the background. If there is a light cover of clouds where you can't see where the sun is but it's still producing a significant amount light then I would wait until just before the "golden hour" because otherwise, even on a light overcast day, the sun will still create harsh shades of highlights that will make your background inconsistent and uneven. Again, you don't want to deal with that in Lightroom or Photoshop.
Below is a double exposure that I initially thought about while I was shooting a wedding.
I was doing the "getting ready" photos. The bride had just gotten her dress on and I was shooting away. I noticed the lights were off and the window was quite big so I moved into position to create a silhouette of her profile using the large window as the background.
When after importing all of the photos into LR, I made sure not to format them off of my card.
I waited for an "overcast" day then went out and shot.
I used the 5D Mark lll 35 1.4 Art & 50mm 1.2 for these shots.