The basics I suggest start with are:
1. Check fuses. I recommend use a multimeter and check for 12V on both sides of each fuse. Connect neg lead on a good clean ground and pos lead on the fuse clips, not on the fuse itself.
2. Check this short wire is providing a very good ground and the metal under the terminals is scratched bare metal. The wire going straight down from that bolt on the fan is the ground wire for the relay in the cab, and it may be attached on a different bolt on your truck. On the fan is where I decided to connect it on my truck.
3. You're hearing that clicking only when high speed is selected, is that right? The switch is all the way down when it is on high. If clicking only on high speed then that may indicate your high speed blower relay is at least coming on. On high speed, the 12 gauge Orange wire that is plugged into the CIG position on your fuse panel goes to the relay, and comes out of the relay on the 12 gauge Purple wire that goes to the blower motor. So make sure that Orange wire is in good condition and plugged into the fuse panel.
4. Check that the motor runs when it is not installed and out in the open, by using something like alligator clip test wires to connect it to the battery. Note the wires will get hot unless they are pretty heavy duty. If they are light duty you can clip onto the case and other end on neg battery terminal, and another wire clip onto the pos battery terminal and just touch it to the power terminal of the motor briefly. Wear gloves. You can also use jumper cables if you're careful where you touch them. Test that the motor runs at all under power. This is a test with the motor out of the truck because of what Sheepdip mentions, there could be something binding and stopping the motor from getting started spinning. You need to know if you have a bad motor or something wrong with wiring.
5. On these trucks it is common for the connector that goes on the back of the fan speed switch to go bad and melt. Check the condition of the wiring, and look very critically at that connector. Make sure all the terminals are engaged fully into the plastic connector.
Please let us know what you figure out, and if you run into any questions.