I've worked out what the issue is

If interacting with the singleton MicroBit instance via a reference or pointer, setting up event listeners doesn't work.
So, the solution is to use a global variable for it.
Perhaps this should be reported as a bug in mBed OS...

source/main.cpp

@@ -17,36 +17,38 @@
 
 #include "MicroBit.h"
 
-MicroBit micro_bit;
+MicroBit ubit;
 
 
 class EventThingy {
 public:
+    EventThingy() {
+        ubit.messageBus.listen(
+            MICROBIT_ID_BUTTON_A, MICROBIT_BUTTON_EVT_CLICK, this, &EventThingy::event_handler_a
+        );
+
+        ubit.messageBus.listen(
+            MICROBIT_ID_BUTTON_B, MICROBIT_BUTTON_EVT_CLICK, this, &EventThingy::event_handler_b
+        );
+    }
+
     void event_handler_a(MicroBitEvent) {
-        micro_bit.display.image.setPixelValue(0, 2, 1);
+        ubit.display.image.setPixelValue(2, 2, 1);
     }
 
     void event_handler_b(MicroBitEvent) {
-        micro_bit.display.image.setPixelValue(4, 2, 1);
+        ubit.display.image.setPixelValue(2, 2, 0);
     }
 };
 
-EventThingy eventer;
-
 int main() {
     // Initialise the micro:bit runtime.
-    micro_bit.init();
-
-    micro_bit.messageBus.listen(
-        MICROBIT_ID_BUTTON_A, MICROBIT_BUTTON_EVT_CLICK, &eventer, &EventThingy::event_handler_a
-    );
+    ubit.init();
 
-    micro_bit.messageBus.listen(
-        MICROBIT_ID_BUTTON_B, MICROBIT_BUTTON_EVT_CLICK, &eventer, &EventThingy::event_handler_b
-    );
+    EventThingy eventer;
 
     while (true) {
-        micro_bit.sleep(10); // 10ms sleep, or 100Hz tick rate
+        ubit.sleep(10); // 10ms sleep, or 100Hz tick rate
     }
 
     // TODO: potentially remove this call, if clarified that it is not required.