THe method I used for fixing my LED handle light may no longer be possible depending on where you live.. You will see why in a bit.
First remove the handle. Depending on who made it the light will be in either the top or bottom mounting.. In many cases there will be a 'Disconnect" just behind the mount.. Tie a string or clamp the wires RV side of the disconnect to insure they do not get lost while you have it on the bench (Picnic table makes a good bench)
IF LED.. Measure the value of hte resistor with a multi-meter. Mine was 150 ohms. it is now 450 ohms THIS IS IMPORTANT.
I got a new LED at Radio Shack (That's the impossible part) I can only give you ON LINE sources for LED's now days (All ELectronics). unless one of the few remaining Shacks is near you.
Carefully De-solder the old LED, and insert the new. bend leads slighty and TEST. NOTE: if you put it in backwards. NO LIGHT If it works, Solder and clip the leads and re-assemble.
Now I've done two RV's Mine and Fred's (you need not knwo who Fred is)
Mine had a polorized connector in the wall so I had to test and then solder
Freds has two non-polorized so I was able to solder then hook up ... Test,, and reverse if needed.
My original LED lasted just a year or so. the first replacement (Same resistor) even less. the second replacement (New resistor) is like 10 years now and still going strong. I* also went with a JUMBO, HIGH BRIGHTENESS LED (Had to drill the hole in the reflector a bit larger) but that's all optional.
Oh you can also choose the color.
If you wish to post the specifications (Forward current and forward voltage) of your LED I can calc the proper resistor but 450 to 500 should work for MOST leds.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times