I always allow patients to undress to their comfort level. Starting off in underwear and socks is a popular choice. Some patients like to trade their shirt for a gown because it helps them get into the role.
If a patient wants to start off fully clothed, I could have them remove their shoes to be weighed and then hop up on the table. If a patient really wants to keep their shirt on, I could work around their shirt. I have never had anyone request this.
If they want to keep their shirt on as long as possible, I could examine as much as I can with their shirt on, and then move to lower extremities before returning to their upper body and asking them to remove their shirt. I like this idea because it preserves an air of modesty at the beginning of the exam.
Probably the most realistic option is to ask the patient to remove their shirt while I examine their upper body. Then they can have their shirt back before we complete the rest of the exam. But no patient has ever requested this either.
My preference is that once an item of clothing is removed, the patient doesn't get it back until the exam has concluded. I also like when on YouTube the practitioner asks the patient to remove an article of clothing and then doesn't immediately address that newly exposed body part. It's as if they are trying to undress the patient as much as possible. In reality, their mind is probably racing as they try not to forget any steps.
I think most role play patients have at least a bit of exhibitionist desire in them. As a role play doctor, the experience for me is more about the overall power dynamic than the excitement to examine any particular body part.