I got four of these white LED reindeer on eBay. They each run from a 36V DC power supply rated for 130mA, but the reindeer only draws about 70mA on average.
I’m not exactly sure how the twinkle effect is implemented circuit wise. There are several single LEDs along the rope light length that flash on briefly about once per second. Each time that LED comes on, a length of rope light associated with it goes off. Perhaps the twinkle LEDs shunt the other LEDs off.
There’s no obvious controller with these lights and the cable from power supply is only two wires. It’s definitely not one of the polarity reversal light sets that have become more common in the last couple of years.