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Yep - so many wires and ECUs in modern cars! They use way more juice on sleep/off than old cars did, even if everything is working correctly. And if 1 little thing isn't quite right... nightmare.
5a charger will do you fine. Consider fitting a quick connector so you can plug it in regularly and keep the battery topped up. A good smart charger like the mxs5 can be plugged in indefinitely without doing any harm.
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