There is a light on the left fender of my tractor which is on (brightly) all the time. It is a separate light from the flashers. Is this supposed to be this way? I find no mention of it in the manual.
Try this, There are two wires going to the tailight, Disconnect one (I forget which color) It's the one that's hot when the key is on. Then leave the one that's hot only when the lights are on.
I have an L3000DT also and that light is always on when the key is turned to the run position. I thought it was a warning light to let people behind you know that the tractor was running.
I don't see a problem with the light. If you don't want it on take the bulb out of the socket.