You have a few problems to solve besides making the square wave.
Let's talk about your LEDs for a moment. You state they are 10W COB type, nominally 12V. You didn’t provide a datasheet, but we can do some estimating anyway.
This class of high-power LED needs about 800-900mA of regulated current, with a forward voltage of about 12V for each LED COB set.
Problem is, like all LEDs, these large high-wattage COB units are current devices, and their forward voltage varies from unit to unit as well as with temperature and forward current. Because of these characteristics, you cannot connect them to a supply without current limiting, otherwise you will destroy the LEDs.
Next problem: how to drive them efficiently? The trick is to minimize IR drop losses as much as you can. One way is to connect them in series and feed them with a higher, yet current-controlled voltage.
Say you want to run 3 of these for a 30W light (that's pretty bright. is that your intention?) Connect them in series, then drive them together with a 36V LED dimmable driver rated for 800mA or so. These modules are available with a variety of voltage inputs, 9-15V boost up to 36V is common, as are supplies that work directly off AC power. I'll leave the searching and shopping up to you. Meanwell is a quality vendor for this.
Now, why dimmable? Because we will use the LED driver's dimming input to switch this thing on and off at your desired 64Hz.
Making 64 Hz
So now we get to your question: How to make 64 Hz? The NE555 timer (or even better, the LMC555 CMOS version) can do this easily. The 555 frequency is set with just a simple RC network. It can also be easily adjusted for duty cycle with the appropriate circuit - this might be worth experimenting with to reduce power consumption. Finally, the 555 can run directly off 12V, which could simplify your power supply.
Could you use a microcontroller? Sure, but why? It's definitely more work. Software, power supply, support circuits… more than is needed.