Your proposed circuit will not work. Let's say a single three LED string draws 20mA, then 24 strings in parallel will draw 24 × 20mA = 480mA.
Now take a look at the datasheet for a typical 555. Although the maximum output current for the 555 is not explicitly mentioned, the 'Low Output Voltage' parameter on page 3 is only spec'd up to 200mA. This means the 555 will not be able to higher sink currents than that.
What you need is a driver stage, a transistor that can be controlled by the 555 and can drive the required current. Simplest is to use a MOSFET, which is perfectly viable with a 12V supply voltage. Because you didn't mention the exact LED current, I can't propose a transistor part number, but the circuit looks like this:
simulate this circuit – Schematic created using CircuitLab
Actually the below may work too, but I can't test it. The discharge pin is open collector and inverted from the output pin. The MOSFET again inverts the signal, hence the BJT from the circuit above can be eliminated.
simulate this circuit
For selecting a proper transistor, look for I(D) being larger than the total expected LED current. Make sure you have some head room, maybe a factor 1.5 - 2 or more.