If you have access to the factory shop manual, there are good troubleshooting steps at testing the cooling system.
The clicking sound does sound like the relay working but the contacts inside could be corroded. (Fairly common problem on a bike this old)
Before attempting to clean the relay take a volt meter to the output side of the relay. It may be trying to work, but may not be sending 12V to the fan.
With the relay off of the bike, spray electrical contact cleaner on the internal parts.
Re-install the relay and re-test with the V. Meter. If it works, great, if not replace the relay or get a fan switch.
If you operate your bike in a warm climate, it may make sense to install the well documented fan switch. Depending on the climate, some owners leave the fan on all of the time.
I personally like to have the relay working as intended, if the cooling system is working to specification, (I.e. thermostat, radiator, water pump, and hoses functioning properly) the fan is adequate at keeping the bike cool.