Wait. What? Mine had the chime on the back, the wires were routed through those little white tags! What a strange thing to change.
Which means I'm out of my depth on this one.
There's not a lot of room in the case for something as large as a speedo chime. Removing the PCB won't tell you much, as the plastic behind it is fairly solid. Plus, you'll release the tachometer mechanism when you take the screws out, which is tricky to realign.
To peek inside you have to remove the clear front panel, the speedo and tachometer needles, then the back panel. Be gentle when removing the needles, they can become brittle. Don't touch the black panel with your fingers, it's a matte finish and you'll leave shiny marks.
It's possible your speed chime is elsewhere! I'd guess it's near the wiper linkages, that's where the lights on squeaker and a bunch of other boxes are.