12 volt tap getting hot

Possibilities:

1. Your wire is too small for the load you are trying to operate...choose a larger wire size.

2. You have a short somewhere in your system...verify amperage draw using amp meter and compare actual draw with design draw of lights.

What wattage are the lights? 16ga wire is max @ 25A....that would be 300W....could be a bad connection...check the amp draw with your ampprobe...Are you sure it's a 12 v connection ?....Golf carts are generally 36v or 48v...

I used the first 2 6 volt batteries for the tap, and i will use 8 ga. wire to the bulbs

Many golf carts have 8 volt batteries. Are you running 2 wires or using the chassis as ground. Make certain you have 12 volts to ground. 16 ga wire should be sufficient for one headlight, 12 ga if you run both lamps from 1 wire

Make sure there is a suitable circuit protective device that will disconnect on over-current!