Without seeing your existing Rule or Form, it should still be relatively straight forward.
Consider the Rule that is hiding the Panel and Controls.
If "X" is True => Hide Panel
That means that if you wanted to make a validation rule inside of the panel to consider it's visibility, you'd need to reverse the logic!
If "X" is False => Validate Control
Additionally, because you want validation to fail if the field is empty you can combine that idea with the first part:
If "X" is False AND This Control is Empty => Control is Invalid!
In practice the rule would look something similar to:
YesNo_Control_Reference && isNullOrEmpty(People_Control_Reference)
Here is a simple mockup using a Yes / No checkbox and a Panel with a People Picker Control inside of it:

Here is the Rule for the Panel:

(Notice the "!" at the beginning of the Control Name Reference. That 'inverts' the boolean value of the control. So an Unchecked Control will equal true instead of false, and a checked control will equal false instead of true. This way the Panel stays hidden until we check the box!)
Now we just need to add a rule to our People Picker Control:

If you click on the little 'F of x' (aka: f(x)) button, you'll be presented with the Formula Builder where you'll have access to all of your Control References and Runtime Functions which you can easily insert into your formula as shown.

(Note: For a Control to show up in the 'Named Controls' tab, it must be given an actual name otherwise it will not be there. In this case I have named the Yes/No Control as 'Show_Panel')
Now when you Preview the form, you'll see no Panel:

Until you check the 'Show Panel' box:

If you try to save without putting something in there, you'll be greeted with an error:

Inserting a valid person though will allow you to pass the validation test:

I hope that this helps you along your way.