Clasic failure symptom of the OD relay is that it audibly clicks but does not pass current to/from the solonoid because of bad solder joints, resolder it. I doubt that a bad solonoid would cause the bulb to fail, the bulb however may be bad. When OD is disengaged (in 3rd gear) voltage source for the bulb is actually 12V through the solonoid to the bulb then to ground.

You should easily hear and feel the solonoid work if you stick your head under the car while someone else pushes the button, car parked, ignition on, no need to start engine.
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David Hunter