It's taken me ages to get back to this, but I've found that with the "disable outputs when off" setting, the output does change in a detectable way. Using my multimeter, I can see that when it's on, the optical output has a frequency of 1413 KHz. When I switch it off, that drops to 1323 KHz (this is what I was missing when I first looked at this - with "outputs always on", this stays at 1413KHz). The 'on' frequency changes when playing (to around 1964KHz).

I'm not entrely sure how I'm going to do this, but these differences are measurable, so I could contruct something to switch the amp on/off. I'll figure something out and let you know how I get on.