Will Check Engine Reset After Air Pump Replacement?

I replaced the Secondary Air Pump and Air Pump Control Valves on a 1996 328i with OBD-II codes P1423 and P1421. Will the check engine light reset automatically?

The replacement pump and valve are operating correctly, no leaks in the vacuum lines. I've driven 180 miles, 16 engine restarts (5 cold starts) and several trips of either highway or city driving lasting over 15 minutes. But still the light stays on. Is clearing the only way?

OBD-II scan says there are no faults, but it still has a history of P1423 and P1421.

<>
When I say cold start, I mean overnight cool-down, but the temperature is still 70°F in the morning.

I believe the air pump vacuum check valve failed first. It was very coked and stuck open, and could not be unstuck despite many cleaning attempts with brake cleaner and WD-40. When I gave up, it would actuate, but not return to a sealed, normally closed position.

Next I discovered the air pump was dead. I was fooled because when I start the car, the air pump vibrates and the snorkel hose makes a sucking sound. The pump was dead, corrosion at connector and seized motor. Engine vibration made the pump shake. Stuck-open air pump vacuum check valve allowed air flow between snorkel and the exhaust manifold.

When OBD-II check engine light is cleared, it resets the computer. There are 8 (?) faults that go to an 'unknown' status until the car is driven and the history adds up. Either the history is OK, and the status changes from 'unknown' to 'pass'. Or, if 3 faults 'fail' or remain 'unknown' after some time, the check engine light will light.