Where does Magento implement methods?

Two possibilities here:

Block method

The getBrandImageUrl is a method defined in the block.

To find out the class of the block you can call:

get_class($this);

Magic method

The method getBrandImageUrl is a magic getter.

Thus it is not explicitely declared anywhere in the code.

As most of the Magento classes extend Varien_Object the code that makes that method available can be found under lib/Varien/Object.php :

public function __call($method, $args)
{
    switch (substr($method, 0, 3)) {
        case 'get' :
            //Varien_Profiler::start('GETTER: '.get_class($this).'::'.$method);
            $key = $this->_underscore(substr($method,3));
            $data = $this->getData($key, isset($args[0]) ? $args[0] : null);
            //Varien_Profiler::stop('GETTER: '.get_class($this).'::'.$method);
            return $data;

        case 'set' :
            //Varien_Profiler::start('SETTER: '.get_class($this).'::'.$method);
            $key = $this->_underscore(substr($method,3));
            $result = $this->setData($key, isset($args[0]) ? $args[0] : null);
            //Varien_Profiler::stop('SETTER: '.get_class($this).'::'.$method);
            return $result;

        case 'uns' :
            //Varien_Profiler::start('UNS: '.get_class($this).'::'.$method);
            $key = $this->_underscore(substr($method,3));
            $result = $this->unsetData($key);
            //Varien_Profiler::stop('UNS: '.get_class($this).'::'.$method);
            return $result;

        case 'has' :
            //Varien_Profiler::start('HAS: '.get_class($this).'::'.$method);
            $key = $this->_underscore(substr($method,3));
            //Varien_Profiler::stop('HAS: '.get_class($this).'::'.$method);
            return isset($this->_data[$key]);
    }
    throw new Varien_Exception("Invalid method ".get_class($this)."::".$method."(".print_r($args,1).")");
}

The first case is the magic getter, next one is magic setter, then magic unsetter and finally magic has.

So in that case, the block is being assigned a brand_image_url dynamically by one of the following call:

$block->setBrandImageUrl($foo);
$block->setData('brand_image_url', $foo);