I'm generally not a fan of LED panels in Christmas displays, but I have seen a couple of displays where they were used as a way to show different "decorations" and that did look cool. Of course everyone has their own likes and dislikes and I'm good with that too. :)
Yes, if you apply 36V DC (or as close as you can get) to the lights and only half light up, that will be one of the newer polarity reversing sets. If they all light up, then a DC supply is what you need.
Does the box mention that it has flashing modes? If so, is there an MFC (Multi Function Controller) between the power in and light set?
Some of the 36V power supplies just supply 36V DC. Others have the MFC built in and reverse the output polarity for the flash modes.
I want to make a "spider victim" (cocoon) prop. Might try it with one of the cheap small skeletons I got from Woolies. I have some of that white wadding that I can possibly stretch out to cover it. Would be good to animate it - maybe just twitching a little.