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My XK 2011 was sitting in the garage for 20 days without driving while I was away. No Ctek connected. But I do have a fairly new flooded type battery in the car. 20 days non usage was no problem. Car started and behaved normally after starting.
Br
ter
This shouldn't be a problem unless you have some draw somewhere. Also you have a new battery so that helps. What would be interesting is to check the voltage prior to start after 20 days.