If you can find a GITD self-glowing silicon bumper, that would be even better.
Very few side click lights have an illuminated switch button beacon thing. I think maybe the Nitecore MH20, Manker, maybe the Noctigon M43.
I wonder if this is because manufacturers are worried that a constantly lit LED will burn out. At an LED lifespan of 50,000 hours, that is 5.7 years.