"Demons Are Troubling You. What You Need is Some Harp Music!' Said Only 1 Person Ever

Now the Spirit of the LORD departed from Saul, and an evil spirit from the LORD terrorized him. Saul's servants then said to him, "Behold now, an evil spirit from God is terrorizing you. "Let our lord now command your servants who are before you. Let them seek a man who is a skillful player on the harp; and it shall come about when the evil spirit from God is on you, that he shall play the harp with his hand, and you will be well.' So Saul said to his servants, "Provide for me now a man who can play well and bring him to me.' (1 Samuel 16:14-17)
Can you see what's wrong with this picture?
In the previous verses, Prophet Samuel has just anointed David. The Spirit rushed powerfully onto David, and the Spirit departed from Saul. David's rise begins, and Saul's descent has begun.
It was obvious to onlookers that Saul was being tormented by an evil spirit. This should have given Saul pause. It did not.
Did Saul examine himself to see if he was in the faith? No, he didn't.
Instead, Saul addressed the symptom. Let's soothe the demon, not investigate why I have a demon. Saul did not appeal to the LORD, he did not pray, he did not sacrifice.
A band-aid on a gushing artery will never solve the problem.
Here is another resource in which we look at practical ways to examine ourselves to see if we are in the faith. JC Ryle's first chapter in his book Practical Religion, the chapter is called Self-Inquiry. Ten questions for self-examination.
Examine yourselves, to see whether you are in the faith. Test yourselves. Or do you not realize this about yourselves, that Jesus Christ is in you?—unless indeed you fail to meet the test! (2 Corinthians 13:5)
Saul failed to meet the test. Christians if they are true believers will never have the Holy Spirit completely removed from them. God's hand will never completely release them, they (we) can and do endure seasons where God has withdrawn temporarily.
Grace To You: I Feel Abandoned in My Trial
Ligonier: Grieving the Holy Spirit
Mike Ratliff: When God Leaves us to Ourselves
Naylor's Heart Talks: When God Withdraws Himself
The good news is that if one is a true Christian, the withdrawal in New Testament times is only ever temporary. Naylor again:

If God apparently withdraws from us, it is only because he sees that we need to be left alone for a season. He sees that the heart must be drawn away from selfish interest; and when this is accomplished, he comes back and reveals to us anew the fulness and richness of his love.

Saul sinned. He never took spiritual inventory. He never went to the source. He only salved the symptom. William Congreve famously said, "Musick has charms to soothe a savage breast," but the savagery always returns. Repentance and dependence on the LORD will quell the terror. Harps only go so far.