How to build simple 12v .5a regulator
LEDs are current driven devices, not voltage driven. In other words, it is not the voltage provided to the LED that matters (except peripherally), as the current allowed through it. 

Intensity of an LED is controlled by regulating the current, or by using Pulse Width Modulation of variable duty cycle (on-off time ratio of pulses) with a predefined, fixed on-state current. 

The question does not specify which specific 12v .5A LED setup is to be used, so it is conceivable that the set-up may already have dimming circuitry built in - LEDs by default are not 12 Volt devices, so there must be some additional electronics in the setup.

If the LED setup does provide a dimming interface, then that should be used to alter the intensity. 


Some LED units contain inbuilt constant-current regulators and favor PWM for control
Others have their own remote control protocol (and control device) - less common
Yet others are essentially just LED + resistor in series, so voltage, current or PWM based intensity control will work


If the LED has integrated current regulation and a PWM interface, a microcontroller circuit would be recommended, to modify PWM duty cycle as per requirement.

For the type of LED setup with just current limiting resistors in there, both voltage and current regulation are options, voltage regulation perhaps being more effective. 

The additional stated requirement is that the LEDs must be driven brighter than default when the ambient light gets low.  For this, you may need to put together a boost regulator, to raise available voltage to a higher value, and vary LED intensity through a microcontroller program as per some set table, in relation to the solar panel's power output (i.e. the ambient light). Without additional information about the solar panels and associated circuitry, it is not feasible to speculate further. 

Regarding input voltage from the solar panel exceeding the rated 12 Volts of the LED strip: LED strips with integrated resistors are quite resilient to a small overvoltage, but you'll only know through destructive testing. Yes, as the question rightly mentions, a 12 Volt Zener diode connected in reverse bias as a shunt at input would be one way of limiting supply voltage to the LEDs.