Hard to tell if there is a single wrong connection from your description. Actually, that's not correct. If any one wire is connected wrong, then another has to be connected wrong as well. So there are at least two misconnections. Surely the new switch came with instructions and a wiring diagram?
What year truck? Your sig suggests a '63, but that would have a factory turn signal switch. Keep in mind that you will have two wires going to the front turn signals, and two more wires going to the rear turn signals. You must also make a connection to the brake light switch. All of these are independent of the park/tail light circuits.
My suggestion would be to disconnect everything and start from scratch, carefully following every step of the instructions.
Joe
