Opening the vacuum hose would normally make the engine run lean. If the AMM starts flashing the light, it means the added air was needed. A steady ON light means the mixture is too rich. A steady OFF means a lean mixture. Since your test light is always on and the AMM adjustment can't compensate, you need to find why the engine is running rich.

My first thought is a problem with the fuel pressure regulator. Check the vacuum hose to the FPR for looseness or splits. These would cause the FPR to set maximum fuel rail pressure and the mixture would be too rich. If the hose is ok, smell the hose and the FPR vacuum nipple. You should not smell gas. If so the FPR diaphragm may be leaking. The best test would be a pressure guage on the fuel rail but most of us don't have one of those.

Good luck and let us know how it goes.