The first thing I would think is a burnt bulb. This could happen if the marker lights are dual filament because the blinker would still show. I don't know if they are, but stopping at Auto Zone to look at a replacement could answer that question.
If a filament burnt and then shorted across the poles, or any other weird things that happen with lights, that one could be shorting your circuit. Could even be water in the light....
Only real way to test would be to remove (or unplug) all four marker lights and plug them in one by one til you find the one that shorts the circuit.
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