Here are a few things to check. I noticed that after the starter relay was clicking, your instrument panel "reset" and did the needle sweep. That happens when power is applied (or reapplied via a voltage dip) to the panel.
The ignition switch and the key switch relay are both involved in getting power to the panel, along with good grounds of course, so a few things could cause power to "dip" that much when starting the bike:
1. poor battery ground or harness grounds (in the tail area). Don't overlook this.
2. faulty ignition switch - it supplies battery power to the instrument panel via the key switch relay
3. bad starter, which draws too much current and makes the battery voltage dip too low to keep the starter relay energized (ie, the clicking) and to have a minimum power threshold for the instrument panel.
These assume your battery is good, as you mentioned. Just some ideas to get you started.