As there is apparently nothing laid down which specifies who is to be commander of the aircraft under such circumstances then it remains important to establish that prior to the flight.
If there is nothing preventing the new member flying the aircraft as PIC with passenger(s) why are you calling the flight a "checkout".
To be PIC, the pilot must be qualified in every respect to be so. That means being licensed, rated and (what we are talking about here) complying with the club/group rules as well as being properly insured.
I would recomend that your group rules very clearly specifies who can be (who is insured to be) PIC of the aircraft. Then there can be no doubt as to who can be PIC.
Giving someone instruction in an aircraft during flight does not automatically make the flight Aerial Work. There is no requirment for all instruction to be completed by a licensed instructor. If the pilot is qualified to fly the aircraft, there is nothing preventing a non-pilot teaching them how to use a GPS unit during flight.
It is true to say that insurance companies do not make the law. However, since insurance is now mandatory, the law says you have to comply with what the insurance company decides.
I would be very surprised if an insurance company permitted flight training on type by a non-qualified instructor - FI / CRI. Therefore unless the new member was already qualified and able to fly the aircraft concerned, i.e. the checkout is merely a confirmation of the pilot's claimed ability I would recomend that a suitable FI / CRI be tasked with the flight training required.
That is why if you read my previous comments, the flights were operated as an recorded as a flight by two qualified pilots - a PIC and a co-pilot. If the PIC does not like what they see at any stage, they can legally take control of the aircraft. The co-pilot can fly the aircraft but the PIC is responsible.