Parking/Running lights should not be doing anything just because you are charging your Chassis battery, or jumping the battery, since you don't have them 'on'. If so, you may have some issue that is beyond what you are suggesting as simply a dead/low battery.
A voltmeter on your battery will reveal it's status, but should be in a range well over 12volts, probably near 12.8 fully charged. When it falls in the 10s or 11s, it may not have enough power to even turn on the lights, or provide power to the starter. Sometimes a dead 'cell' within the battery can make the battery seem 'good' with a voltmeter reading, yet 'fail' when trying to power the starter. When a load is applied, the bad cell brings down the whole battery.
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