If t'were me I'd have it in bits to see if I could see the copper tracks.
They probably put 3 leds in series across the 12V, or something like that.
(Though 64/3 doesn't go!)
There might be some small resistors built in to the board.
Characteristics of LEDs are something like this
where at the knee, for a white led you'd expect 4 volts ish at 20 - 30 mA.
So if the voltage goes up the current does too but quicker than it would for a straight resistor.
Leds fail by overheating though so there's time factor. If you can just check the current is within range you're fine.
A note about the power supply though - if you use a $5 plug-in DC supply it might not be smoothed. The average voltage may be OK but it'll look like the red line here:

My green lines are meant to show what happens if it IS smoothed, by a big capacitor. It works out that you need darned big capacitors! The humps are at twice mains frequency, so 120Hz for you (100Hz in uk).
(Car batteries don't care, they act just like a huge capacitor)
If there's NO smoothing the LEDs would go OFF 120 times a second whenver the voltage on each one drops below about 3V.
If the Average (rms) voltage is 12v, that's about 70% the way up the sine curve, so you can see that "below 3V" is quite a long interval per cycle.
I have a reading lamp with LEDS. I can't see the flicker, but a camera
can ( so can its LCD screen!) It's useless - except for reading by!
The answer is
usually a Switched Mode Power Supply, like computers use, as do some table lamps, because they flicker at much too high a rate to worry anything.