M104 air pump run after warm
 

1995 E320 with 224K
When I start the car cold, the air pump works for about 2 minutes, then cuts off for 2 minutes. But then it will go on again for 30 seconds, go off for 2 minutes, then on again for 30 seconds and finally shut off for good.
Additionally when I start the car cold, o for a 2 mile drive then pull to a stop, the air pump will come on for 30 seconds.
What/where is the brain that controls the air pump? I supposed that is what is faulty that I need to get at. Too bad this car has a serpentine belt, otherwise I would bypass the air pump altogether.
Unrelated or perhaps related, I've had a code 4 & 26 for years which is related to the upshift delay system. The green vacuum hose running to the trans is not holding vacuum and it is too difficult to get at the upshift cable mechanism so I plugged the system at the firewall. Codes came back So I assume the upshift circuit is also faulty because the firewall junction for vacuum tube is open/sucks even when car is warm/hot.
Any insight appreciated.

Honestly this sounds somewhat normal. The (rebuilt) air pump sometimes cycles briefly at idle on my 300E after the initial 2 minute running.

Also, you can remove the smog pump and purchase a shorter belt, plug the lines, and go on your merry way.

The DM will cycle the air pump to check its function after the 02 sensor has warmed up enough for it to read the additional air, its normal.

The upshift delay code is set when the engine RPM doesn't reach the specified value when the engine is cold and the delay is active.