Muddy Poppins wrote
... the sound is produced by an internal spring mechanism...
I bought a rather disappointing job-lot last week. I was reflecting that I'd paid a bit more than I should have, and ought to have looked more closely at the wear and tear evident in the photos, when I picked up the very last Annie/Clarabel in the lot and turned her over to see how old she was.
One double-take later, the lot suddenly seemed rather more interesting...
Twangy Annie - Under the Hood
As seen in Muddy's Video, this is what she looks like underneath:

Inside the chassis, there's a gear-train:

On the end of the gear train there's a partial gear with only five teeth, covering about a quarter of its circumference:

As it rotates, this partial gear strums along a spring that's anchored (at the RH end in this photo) on another sub-assembly screwed inside the body shell:

The end of the spring that's not anchored to the frame pulls on a bar on the other side of the sub-assembly:

This bar gently presses down on a shell-shaped metal sounding-board:

So the partial gear twangs on the spring, the spring wobbles the bar, and the sounding-board amplifies the twanging noise, which does sound a bit like chuffing (but not a lot!).
I agree with Trevor379, it does seem strange that this feature doesn't appear to be mentioned anywhere on the outside of the box of the Thomas Adventure Set (Tomica World #7408) in which it was found.