Many thanks guys - that did the trick! I seem to remember coming across those clips before somewhere else in the car, and seemed to just luck into getting them apart. It's all so much easier now I know how it works!
Now all I need to do is get the black backing plate off to get access to the circuit board... I've unscrewed all (six?) screws holding the black plate on, and I can see there are two clips holding it in at either end, but is there anything else I need to loosen? Even if I release the two clips, the black cover doesn't seem to come away from the circuit board, and I don't fancy just pulling it in case there's a clip hiding somewhere I don't know about
I guess now is probably as good a time as any to ask if what I'm doing is actually possible! I've lost sound from the speaker in the instrument panel, so I'm getting no beeps when I leave my lights on, or from my reversing sensors, despite the reversing sensors all activating properly. So, I'm assuming it's either a duff speaker, or a dodgy connection to the speaker, and I was hoping I'd be able to check it by getting the instrument pack to pieces. Fingers crossed...
