Thank you!The second click is the relay going to warming glow plugs. That is much slower than what your sound is. The constant click is a fuel solenoid switch.
You need to check 5 things.
1. Principal ground wire connection going from battery to chassis.
2. Battery connections.
3. Glow plug rail nuts which reside along the valve cover to make sure none are loose.
4. Glow plug ground connection at end of glow plug rail to make sure connection is viable..
5. Starter solenoid connections.