If the hammer fall test is done correctly, a proper trigger assembly should not allow the hammer to fall if the hammer is cocked with the trigger held back and then the trigger is released. The hammer hooks should "transfer" and hold.
So, if this is the case, meaning you released the trigger and the hammer fell, you need to replace/repair the trigger assembly.
They used to be cheap enough to just replace as a unit, but I don't think this is true any more.
Pretty obvious suggestions, I suppose, but if the hammer hooks are sharp and even on both sides (L & R), the trigger/sear is the place to start.
And if both the trigger/sear and hammer hooks look beat up, replace both parts.