I think on all my bikes the LEDs for alarm have failed. Reason is they generally are just fitted by a shop and as they are on bodywork the constant vibration just snaps legs off them rather than the LED chip itself going faulty.
Replacing is quite straight forward though it's probably more trouble than it's worth...
Reason is that you have to establish how the alarm is feeding the LED... all LEDs need to be current limited so it's possible the alarm has the current limiting resistor internally. I very much doubt you'll find a resistor soldered to a leg of you current LED.
The other possibility is the LED on the bike has a built in current limiting resistor.. but these are expensive so unlikely to be the route the manu went
I would just leave alone tbh, unless you call up the alarm manu and ask them how the LED is fed... once you know this it's a easy job though
If you went ahead and chose a LED / Resistor and it turns out the Alarm already has a resistor internally your LED would be very dim / not light at all..... if you connected a LED without resistor and it turns our the Alarm doesn't have one either you could possibly destroy your alarm.
If you want to have a bash get a resistor of around 1-2k range I guess.... this would limit current to around 10mA at 14.5V, if it lights but very dim, just halve it's value (and assume the alarm is also limiting). The current you 'set' though depends on LED type used.
edit: if the above blows up your alarm it's not my fault lol.
edit edit: you might just get away with buying a 12v LED (with internal resistor), maybe enough to light even iif alarm already has one... it's probably the safest route where you can't do any damage.