Cleanest way to solar-power a string of outdoor bistro lights
We can guess the 12 LED lamps are wired in parallel, and each has its own individual dropping resistor or driver circuit.  (Because if they were wired in series the power supply voltage would have to be at least 12 times the individual LED forward voltages, probably 15V or more total).
I'd say you just need a 5V supply that can supply at least 1.2 A.
I'd suggest the easiest solar power solution is a &quot;solar power bank&quot; with 1 or more USB receptacle(s). You will need to cut the wire to your lights and splice a USB plug. When you make the cut, take care to test and label the wires to determine which is positive and negative, and match that to the USB voltage.
This search term Amazon solar power bank will find plenty, ranging from $25 up and supplying 2A or more. To determine if they can run all night, check the battery capacity. For example, a 20000 mAh battery is 20 ampere-hours, so it could supply 2 A for 10 hours, maybe not enough to run all night in winter. You also need to have plenty of sunlight all day to charge it. Finally, be aware these units will wear out from repeated charge/discharge cycles. Bottom line: reconsider whether you could find a way to run a wire through your door, window, or wall.