Just to be clear, you're saying the glow plugs stay on permanently when the engine starts... like for more than several minutes ??
I ask because some afterglow is normal... dependent on engine temperature... but I believe it can be several minutes in length for some engines. It improves drivability and reduces emissions.
The relay is pretty smart... it knows, for instance, if you haven't engaged the starter and shuts off the pre-glow... just like your test light shows.