Right, when he gets the advice and consent of the Senate, he shall appoint. Not before then. The imperative is directed at the President, not the Senate.
Wrong again. You have merely restated your initial incorrect assertion. Your premise is invalid; sequence and timing is not equivalent to acting or failing to act. The imperative encompasses both the President and the Senate because the Senate cannot, by deliberately refusing to act, lawfully, i.e. constitutionally prevent the President from carrying out his duty.
Let's try putting it another way:
1. The Constitution is the supreme law of the land (at least it's supposed to be).
2. The Senate is free to make its rules, but Senate rules are not even ordinary laws, much less part of the Constitution.
3. When a Senate rule is either devised or is used to subvert, undermine, obstruct or otherwise prevent the members of the Senate or any other Constitutional Officer from carrying out their mandatory duties, the rule is invalid. The Constitution always trumps procedural rules.