Looking at the Service Manual, (pages 1921 -1930) there is a complete diagnostic exercise to check out the various components in the air pump system. It relies on using the DRBIII tool but mainly to manually switch the relays and valves to perform the tests, so you may be able to improvise. You probably want to check it out for yourself but a summary of the causes is given as:

POSSIBLE CAUSES
AIR PUMP VOLTAGE SUPPLY CIRCUIT OPEN
AIR PUMP VOLTAGE SUPPLY CIRCUIT SHORT TO GROUND
AIR PUMP GROUND CIRCUIT OPEN
CRACKING, MISSING, MISROUTED, OR PLUGGED VACUUM LINES
AIR PUMP SWITCHOVER VALVES
AIR PUMP RELAY
AIR PUMP
POWERTRAIN CONTROL MODULE

Since you say that the pump is running then there probably isn't a problem with the relay etc, but it may be an intermittent connection. So I guess it's probably worth checking out the vacuum lines and valves as listed above.

Following on from aschrager's experience and just for extra information I had a look at the Relay Control Module which is situated in the ECU compartment near the battery. It can be lifted clear after moving the two retaining clips. The module houses:

Air Pump Relay
Engine Control Relay
Traction System Relay
Horn Relay
Fuel Pump Relay

Presumable to save money they have used open framed relays mounted on a PCB, rather than five individual replaceable relays rendering the unit 'unserviceable'. However you can pop the lid off and inspect the innards if required. Interestingly I noticed some corrosion on one of the relate contacts on mine. I would have a look and just check that all the solder joints look intact and that the relays are free to move (after disconnecting the battery of course!).

It’s all much easier if you have an OBD scanner because you can reset the CEL before each test and also see codes that are pending before they are tripped.

Good Luck!

Lifting out the RCM


The RCM innards...