Not sure what lamp that is. The little red key-shaped light I think stays on or flashes when the bike is off. Is it running? any problems besides the light?
If you have the security system try changing the battery in the fob, I have no idea if the key shaped security light will come on if the fob battery is low or not but it might be worth a try.
It is normal for it to come on when you first start any bike. If the bike has the security option, it is normal for it to flash at a slow rate when the bike is off. If it has an alarm system and the system activates, it is normal for it to stay on steady as your turn signals flash.
What exactly is happening and under what conditions.
07 Electra Glide has the security alarm key icon comes on with the ignition. Stays on as long as the ignition is on. I do not have an alarm system. What does the constant "light on" mean?