Short answer. Yes. Rule 119, Section 21 gives the judge two separate grounds to exclude the public: on the judge's own initiative when the evidence is offensive to decency or public morals, or on the accused's own motion, exclude the public from the trial except court personnel and counsel. Your motion does not need obscene evidence to qualify.
What the law says
The judge may, motu proprio, exclude the public from the courtroom if the evidence to be produced during the trial is offensive to decency or public morals.
Rule 119, Section 21 — Exclusion of the public. Read the full provision →
What the law says
He may also, on motion of the accused, exclude the public from the trial except court personnel and the counsel of the parties.
Rule 119, Section 21 — Exclusion of the public. Read the full provision →
Section 21 provides two separate grounds, not one
Rule 119, Section 21 does not treat exclusion of the public as tied to only one trigger. The first sentence covers the judge acting alone: the judge may, motu proprio, exclude the public from the courtroom if the evidence to be produced during the trial is offensive to decency or public morals. The second sentence then adds a distinct, separate basis, introduced with the word also, which is the one that answers your question.
The offensive-evidence ground is the judge's own-initiative power
The first ground in Section 21 is specifically about the judge acting on the court's own initiative, and it is expressly tied to evidence that is offensive to decency or public morals. That ground alone would not cover a request based simply on wanting privacy, since it requires the content of the evidence itself to meet that description, and it does not depend on either party asking for anything at all.
Your motion is its own, independent basis
The section gives you a separate route: he may also, on motion of the accused, exclude the public from the trial except court personnel and the counsel of the parties. This ground is attached to a motion filed by the accused, not to the nature of the evidence. Nothing in this second sentence conditions it on the evidence being offensive to decency or public morals, so wanting privacy is enough to bring the motion.
Who is not excluded even if your motion is granted
Excluding the public under this section does not clear the courtroom entirely. The rule specifically carves out court personnel and the counsel of the parties, who remain present regardless of the exclusion. So even if the judge grants your motion, the trial still proceeds with those participants in the room, and it is only the general public that is kept out, not the people the case actually needs present to function.