The flasher is part of the hazard switch and has been known to fail like this. Replacing the switch should solve this. Another problem is that the bulbs need to be pulling enough current, if they have been replaced with LED bulbs change them back to the OEM style.
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If the bulbs are not original type then they need to be replaced. Replacing the hazard switch should solve the flashing issue if the bulbs are the original type.
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No, if they are original the problem is in the switch/flasher assembly and replacing the bulbs will not change anything. Some owners replace the bulbs with LED lamps and they do not draw the same current.
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Yes, both the hazard and the turn signals are flashed by the same unit in the hazard switch. Replacing the switch should repair both issues.
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