Yes, of course there's a chance it's the breaker. But, it's a very slim one: breakers don't fail that often, especially not in low-amperage applications like the anchor light.
Put a multimeter across the wires to the anchor lite. Use the beeper function (for short circuit). If it buzzes, then the light and wiring
are OK. If it doesn't, then either the wiring
or the bulb are bad. If you had a TDR, you could know which without going up the mast
, but you'd likely have to go up anyway to fix whatever's wrong.
Also, while you're at it, read the voltage at the input and output of the breaker.