Having become quite the p-bass guy in recent times, have been loving the flat-mute thing and spotted a YT video a while ago with Sean Hurley and a strange mute thing on his precision.
Having googled it, it appeared to be a Fender Jaguar mute, added at some point. There were some posts on other forums and websites so, whilst I was on holiday over the past few weeks in the States, I ordered one to bring back, avoiding the postage and import taxes.
Here's t