Are side marker lamps suppose to blink???

SleeperScamp said

So if the bulbs are good (side markers work with park lights on) and they do not blink, then where do I start?

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If one of your turn signal bulbs either in the front or back is in wrong it will make your side markers blink.
Turn your lights on and turn your blinkers on and start pulling turn signal bulbs till the side markers stop blinking.
I have seen bulb sockets shorted as well,but I bet one of your turn signal bulbs is in backwards.