I gave it another try, and also based on some other posts linked above I actually managed now to get the expected GPS WAYPOINT identifiers (ICAO codes):
This worked both with an A320neo with a “IFR Low Altitude” flight plan from LSZH to LSGG (Zurich to Geneva) as well as an Aviat Pitts Special (“as simple as it gets - no GPS, no autopilot”) from some tiny, random airport LFGB with a VFR flightplan to…
Holy moly! Is this some beautiful area: LFGB
UPDATE:
Even the crash sites look gorgeous in this area 
Sorry… where was I? 
A yes, the GPS WP NEXT/PREV simulation variables also worked with an Aviat Pitts Special and a simple VFR flight plan from LFGB to another random, tiny airport LSGR (so no “active GPS system” required in the aircraft).
Including access to the waypoint coordinates that is all I need for my requirements, to figure out the starting and ending location (ICAO code) respectively the information whether the aircraft flew anywhere “near” of any of those waypoints…