In the T1N, many of us have (what i'll call) a European Parking Light "feature" (it's documented in the owner's manual, so it wasn't a surprise).
IF:
we turned our parking/headlights/"P" stalk to "P"
and
turned off the engine
and
flipped the directional handle up or down...
THEN
the selected direction's tail (parking) light would illuminate and stay on.
It was to serve as a "rear outer marker" when you were parked by the side of the road at night, or in the fog.
Perhaps you're seeing something similar?
--dick