Do you have a multimeter and do you know how to use it? Answering this question will shape future troubleshooting tips.
MG has it right. You have a hot lead crossed with a ground...somewhere! Try this, disconnect ALL your lights and turn on the switch. If the fuse blows, the problem is at your switch. If the fuse doesn't blow, reconnect the lights, one at a time. When the fuse blows, you've found the faulty circuit.
Since you've replaced the harness, it is more than possible that while routing it through the car, you've sliced through the insulation somewhere and that wire may be in contact with the chassis. When you energize that wire, boom, there goes the fuse!
Let us know what you find by doing this.
On their death bed, nobody ever said, "Gee I wish I'd spent more time at work!"
'68 Sprite 1275
'76 Midget 1500