If your light uses a filament lamp then almost certainly a continuously-on setup would consume the most power. But presumably your light uses LEDs, which are much more energy efficient.
Your blinker circuit is almost certainly not relay-driven; if it were then the relay activation would consume a lot of power, possibly more than a filament lamp. It could be a timing circuit with a resistor-capacitor combination and transistors but more likely a timing circuit (e.g. 555 timer) which, without looking up specifications, I suspect to be more energy efficient than a RC combination.
I think that with an electronic timing circuit and LED light, a continuously-on mode would consume the most power, and even at a 50/50 duty cycle the light would still consume more power than the timer, but less than a continuously-on mode. For the timing circuit to consume more power than the light it would possibly need the light to be on less than half the time, which probably means it's still useful for being seen but not useful for seeing.