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It should be the glow plug controller, here the diagnostic info if you want to do some testing to be sure.
DTC P0670CIRCUIT DESCRIPTION The glow plug controller has the ability to perform internal diagnostics for voltage and output state of the glow plugs. If the glow plug controller senses an open in the main battery supply to the glow plug controller, or a condition with any of the glow plug driver circuits, the glow plug controller will send an error message to the engine control module (ECM).DTC DESCRIPTOR This diagnostic procedure supports the following DTC: DTC P0670 Glow Plug Module Control CircuitCONDITIONS FOR RUNNING THE DTC - DTC U0073 or U0106 is not set. - The ignition is ON. - DTC P0670 runs continuously.CONDITIONS FOR SETTING THE DTC The glow plug controller detects an open to the main battery supply for the glow plugs, or an open in all 8 glow plug circuits for less than 1 second.ACTION TAKEN WHEN THE DTC SETS - The control module illuminates the malfunction indicator lamp (MIL) on the second consecutive ignition cycle that the diagnostic runs and fails. - The control module records the operating conditions at the time the diagnostic fails. The first time the diagnostic fails, the control module stores this information in the Failure Records. If the diagnostic reports a failure on the second consecutive ignition cycle, the control module records the operating conditions at the time of the failure. The control module writes the operating conditions to the Freeze Frame and updates the Failure Records.CONDITIONS FOR CLEARING THE MIL/DTC - The control module turns OFF the malfunction indicator lamp (MIL) after 3 consecutive ignition cycles that the diagnostic runs and does not fail. - A current DTC, Last Test Failed, clears when the diagnostic runs and passes. - A history DTC clears after 40 consecutive warm-up cycles, if no failures are reported by this or any other emission related diagnostic. - Clear the MIL and the DTC with a scan tool.TEST