If there is a relay for the glow plugs, the contacts may have carbon build up causing the relay to stick in the on position. Pull the relay and see if the light goes out. If the relay is sticking, the motor will still work but the glow plugs will stay powered and no doubt that will do damage. The glow plugs draw a good deal of power and the charging system will have to work harder to keep up with demand.
I've seen this on Peugeot diesels and am just guessing at your situation.
If the light goes out when the relay is pulled, you will need to check if the relay trigger wire is hot, if it's hot you have other issues not a bad relay.
Check for B+ on the relay trigger wire with the motor running and warmed up, otherwise there will be B+ at the signal wire as there should be for start up.