What AMP rating do you have on your GT? Was it new/reman when Keith restored your car or was it reused from before th resto?
I have the 45 amp alternator but can't recall if it was new or re-manufactured. On a day to day basis I don't have any issue though. The AMP gauge shows it is charging the battery and the car starts right up on the very first crank day in and day out. Only when the car sits for several days in colder weather do I have this issue.
Today, for example, I went to start the car this morning after it sat for almost 5 days. The car turned over several times but, after the fifth attempt or so, the battery clearly didn't have enough power left and the car wasn't going to start no matter what. When I got home from work and the car had sat some more, it started right up on the first try. My theory is that the battery is losing some charge when it sits for several days in the colder temps and then doesn't have enough power to turn the car over the few extra times it needs after it has sat. The car starts many hours later presumably because the battery has gained back some charge and the car only needs one crank because it was "primed" in the morning.
Anyway, my theory is that the battery tender would keep the battery at full charge and therefore have what it needs to start the car after being parked for a period of several days (i.e, the battery could handle the few extra cranks required). Then again, maybe I am just flooding the carb when it needs more than one crank to start up

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