Why doesn't the message waiting light flash when there is a message?

If you want to replace a handset or re-assign the designated handset number of a registered handset, you must de-register all the handsets and then individually register each handset.
To de-register all handsets:
Press and hold
FIND HANDSET
on the telephone base for about 10
seconds (until the IN USE light on the telephone base turns on and starts to flash), then release FIND HANDSET
.
Press and release
FIND HANDSET again. (You must press FIND HANDSET
while the IN USE light is still flashing. The IN USE light flashes for
approximately seven seconds.)
All system handsets show
CONNECTING...
The de-registration process
takes about 10 seconds to complete. All handsets show
NOT REGISTERED
when the de-registration completes.
If de-registration fails, you might need to reset the telephone and try again.
To reset:
Pick up the registered handset and then press
/FLASH
.
Press
OFF/CLEAR
and place the handset back in the telephone base.
-OR-
Unplug the power from the telephone base, then plug it back in.
note:
You cannot de-register a handset if any system handset is in use.

After de-registering, proceed with registering process:
If the handset screen does not show LOW BATTERY
or HANDSET X, you will need to charge the handset for at least five minutes before registering to the telephone base.
To register a handset:
Place the unregistered handset in the telephone base or charger. If
PRESS FIND HS 4 SEC ON BASE
does not appear on the handset screen after a few seconds, remove the handset and place it in the telephone base or charger again.
On the telephone base, press and hold
FIND HANDSET
for about four seconds (until the red IN USE light on the telephone base turns on) and then release the button. The handset shows
PLEASE WAIT...
and it takes about 10 seconds to complete the registration. The handset shows
HANDSET X REGISTERED
(X represents the handset number assigned)
and you hear a beep when the registration completes.

I believe that another user has called you and while the phone was ringing, they pressed the message button - and set the lamp.
With the handset still on the cradle, press the message button... read the display. Follow the prompts to cancel or call the message sender.
OR
Pick up the handset, and press the message button. It should call the extension that set the lamp.

The code you refer to is not a standard code. Each vendor or installation is different and the codes can be set how the vendor or site wants them. If the above doesn't work, I suggest you contact the vendor for this info. Or if you have system access, log into the system and find the form Feature Access Codes. Look for the Lamp off code. Dial that code followed by your extension number.

I couldn't find the exact manual for your phone but I would try to re-register the phone. Following are some instructions for similar models of your phone.

*To do this on a non-expandable cordless phone:

• Press and hold the LOCATOR/INTERCOM button on the Base until a beep sounds.
• Press and hold the FLASH/CALL WAIT button on the Handset until a beep is heard.
• When registration is complete, a beep sounds from the handset.
• Wait for 20 seconds after registration is complete to allow the handset to establish communications with the base.

If this fails to help: Remove the AC Adapter from the phone base or wall outlet for a few seconds and reconnect. It may also be necessary to remove the battery from the handset for a brief moment.

Good luck!

That is the message waiting indicator, it is telling you that your Call Notes (Or whatever your service provider calls it's voicemail) has a message waiting. If you do not have a message waiting, you can turn the light of by following these steps:

Resetting the voice message waiting indicator
When you receive a new voice mail message, the new message LED on the top of the handset flashes and
appears in the handset display. In the event your message waiting light gets out of sync with your phone company’s
voice messaging system, you can manually reset it back to the “No messages waiting” state.
Press and hold FIND on the base for five seconds.
Note: The handsets connected to the base will start to beep, however, keep pressing for five seconds.
A beep sounds and the message alert tone is reset.

This may help. It's from the Panasonic help page:

You may try to:

Disconnect AC power adapter from the back/bottom of base unit, then connect it again properly.
OR, to resolve this issue, you have to re-register the handset.

• To do this on a non-expandable cordless phone:
  Press and hold the LOCATOR/INTERCOM button on the Base until a beep sounds.
  Press and hold the FLASH/CALL WAIT button on the Handset until a beep is heard.
  When registration is complete, a beep sounds from the handset.
  Wait for 20 seconds after registration is complete to allow the handset to establish communications with the base.
  If this fails to help:
  Remove the AC Adapter from the phone base or wall outlet for a few seconds and reconnect. It may also be necessary to remove the battery from the handset for a brief moment.
  
  
• To do this on a expandable cordless phone system:
  Press and hold the LOCATOR/INTERCOM button for the extension that is displaying "No Link To Base" on the Base until a beep sounds.
  Press and hold the FLASH/CALL WAIT button on the Handset that is displaying "No Link To Base" until a beep is heard.
  When registration is complete, a beep sounds from the handset.
  Wait for 20 seconds after registration is complete to allow the handset to establish communications with the base.
  If this fails to help:
  Remove the AC Adapter from the base or wall outlet for a few seconds and reconnect. It may also be necessary to remove the battery from the handset for a brief moment.

Press down the "find handset" button until the paging beep stops (about 5 seconds) and this will reset the indicator lights on the handsets.

Press down the "find handset" button until the paging beep stops (about 5 seconds) and this will reset the indicator lights on the handsets.

Press down the "find handset" button until the paging beep stops (about 5 seconds) and this will reset the indicator lights on the handsets.

I had this problem, solved it by going to the advanced settings menu and resetting the handset. I guess the handset got out of sync with the base station after I deleted messages... once reset it was fine.