Yes, if could be the cause of the clicking - when it was installed - but I'm not sure it could be if it was not installed. For example, if it was installed and the pin ends were not quite wrapped once out the other side of the hole if could catch on something.
You must have the SE5, correct? Yeah, that beep and (!) as I understand it also, is the reminder that your parking brake is engaged. At this time you'll likely see 'Parking Brake' scroll on the cluster also. There is a switch just above the parking brake peddle (you have better view and access to it with the lower panel removed), and once this peddle is down (i.e.: parking brake peddle down and holding the bike in place for parking), it pulls the switch that enables the beep, the (!) and the 'parking brake' message on the cluster.
It may be possible your parking brake needs to be adjusted, or perhaps the switch needs a quick look (perhaps tighten, check spring on peddle?). The switch is on the left side near the parking brake peddle. However, since work was done recently on your rear wheel, I would be inclined to check that side of the parking brake cable first - it's on the right hand side of the bike, just below your pipe. Be sure there is enough movement in that side of the parking brake assembly such that it can be released properly when the parking brake peddle on the left side is completely sprung back up. May need another person to manoeuvre the peddle while you check out the movement and range on the other side of the bike. Not sure about the clicking, by at least you have a few things to check which may be the cause (parking brake cable and assembly, cotter pins - get those installed before riding, and I would also do a once over the rear brake assembly - are the pads touching all the time - if you raise the rear wheel off the ground does it rotate fairly freely in neutral?
That is where I would look, given the information we know so far. However, you mentioned the rear brake lights - that makes me think two possible things to check; 1) perhaps the brake lights are actually on and you don't know the difference since they are already bright - check the brake switch. 2) It is possible to have some electrical issue causing the brake lights and the parking brakes to show (!) and emit that beep?
Either way, I hope these suggestions help.
Interesting post, please keep us posted!
Thanks and good luck, looking forward to your next post!
Dean