FAR 61.129 several times uses the phrase “night VFR conditions.” Does this mean strictly flights conducted under VFR at night, or does it include night flights conducted under IFR but in VMC?
"Night VFR conditions" describes the flight conditions, not the flight rules. The PCG says:
VFR CONDITIONS− Weather conditions equal to or better than the minimum for flight under visual flight rules.
If the requirement was to conduct the flight under VFR, the regulation would say "under VFR". For example, 91.185(b) shows that the FAA sometimes makes that distinction (emphasis mine):
If the failure occurs in VFR conditions, or if VFR conditions are encountered after the failure, each pilot shall continue the flight under VFR and land as soon as practicable.
So you can do the flights under IFR in VMC if you like.
Since it specifically says "VFR," you can't be on an IFR clearance, or following IFR rules in uncontrolled airspace. You are never both VFR and IFR at the same time, you can only be one. You can be VMC while IFR, but that doesn't meet the requirement as written in this rule.