The GT has a lithium-ion battery. I should mention from the outset that I have ZERO experience with automotive lithium-ion batteries.
I was touring the Markham facility a couple of weeks ago when I was handed a full-size automotive battery. The battery weighed a fraction of what a lead-acid or an AGM battery would have weighed. I was told that the battery that had just been handed to me was a Ford GT lithium-ion battery. It was then emphatically emphasized to me that I must be extremely diligent about keeping my GT's battery tender connected at all times. I was told that, once the GT's battery becomes fully discharged, it cannot be recovered. It was then explained to me that the front end of the GT must be disassembled in order to access and replace the battery.
Perhaps you might speak with your servicing Ford dealer before doing anything?
Here is a link to a page on the Optima Battery website. The page explains a procedure (Recovery Option #2) that I have used to recover a fully-discharged AGM battery for which my charger would not initiate a charging cycle. I have no idea how difficult it would be to attach your GT's battery in parallel as described in Recovery Option #2.
Good luck!
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