Depends on the purpose of the flight. If its for the revalidation of an SEP Class Rating where the dual flight is required for revalidation by experience then its dual. I will and do quite happily fly this flight as dual in aircraft not fully equipped with dual controls. The RV4 is an example of this.
Whenever I am in an aircraft in a teaching capacity then I am commander and its dual. If I am just going along in a mentoring capacity then the pilot is commander and I log nothing as I am going along for a ride and may be able to add something useful to the pilots experience by giving tips and hints.
You can throw as many scenarios as you want at this. The main thing is to establish the purpose of the flight, agree the terms up front and go and do the flight. There is way to much complication made of this for no real reason.
Speaking as the HoT of an ATO I do not accept any FAA flights that have been logged as P1 where the purpose of the flight was clearly Instruction and in EASA world would be dual as acceptable requirements for any of the courses that we offer as an ATO where P1 time is needed.