For Panasonic cordless 5.8GHz phone with answering, does the charge red LED go off when the handset is charged?

I have the KX-TG5632CM cordless Panasonic buzz. There is a charge light (red LED) that when you place the handset back on the base turns on indicating that the handset is being charged. But it never goes off. I am worried it keeps the batteries in charge and will hurt the batteries. Does yours go off? (Even if you have a similar model, cordless with answering machine, it would help)

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