if you try to go off of just one set of batteries the resistance when charging will make that bank of batteries weak and will fail prematurely
I did this with some small led's (2x .02 amp draw)in my battery room and after about 3 months that set of batteries were weak to the point I had to take them off-line
rather pay $60 instead of the price of a new set of batteries
I'm not going to argue with you over what happened to your batteries, but I will tell you that tapping from a single battery is the way the factory OEM power outlet works on my Yamaha YDRE cart. I will also tell you that my measured voltages on my battery monitor I built for this cart also show that none of the batteries are the same voltage level.
When the charger charges, it has no way of knowing about individual batteries. It looks at the batteries as a single load and applies charge current based on total charge level (voltage). A single battery will only have the effect of changing the resistance of the entire charging string. It will not see any charging current difference to the other batteries since current is the same through each component of a series circuit. However a single battery with high internal resistance can limit total current through the chain. Batteries with lower voltage will also have lower resistance, but the only difference in a series circuit is voltage drop across each battery. Even in perfectly matched sets, this will vary as the batteries age. In my recent round of battery problems. I found one battery that had very high internal resistance due to being defective. It slowed charging time for all the batteries by limiting the maximum current that could be applied to the string. When a healthy deep cycle battery discharges, it's internal resistance decreases (that's why charging current starts out high).
So, I'm going to disagree with Beltman60 on the danger of tapping a single battery in the string for an LED light. I believe his DC-to-DC power supply would drain a cart's batteries due to efficiency losses while providing 12 vdc probably more than a 18 watt LED light turn on occasionally as needed. If you have some other batteries in the cart other than 12 or 6 volt, you have to use a power supply, but Beltman60 and I have different opinions of the nature of healthy golf cart batteries and chargers. He has his reasons and I have mine. By all means, do what feels best for you and gives you the most confidence in the outcome.:thumbsup:
EDIT: Arkaybee, if you are going to install headlights/tailights and use your lights most every time you use the cart. I'll certainly change my suggestion. My comments above are based on a single light with only occasional use.