If you do decide to replace/install a new diode, the are polarity specific .
The 1N4001, looks like a small black cylinder a few mm in diameter and about 5 mm long with a wire lead out of each end .
It should have a thin silver band at one end, if you are replacing the one in the plastic holder, be mindful of which way it was installed .
If you don't, you will have the same problem with the light that you have now .
If you splice it in somewhere in the wire harness, don't solder it in permanently, until you test it, to be sure it's correct .