Hi, welcome to the forum.
Ask 10 programmers about random, and you get 100 opinions
This topic might get flooded with everyone talking about random and what they think is best. In the end, the Arduino random() function which uses the GCC compiler random is not so bad, it pretty evenly distributed.
Sure, you can use that Gaussian library and convert the value to a 0...255 integer for the PWM.
Why do you need something sophisticated for just a led ?
If you want a certain visual effect, then there are easier ways to implement a curve.
Did you know that the human eye sees brightness with almost a 10log curve ? That is a very steep curve. Perhaps what you have in mind will be visually not the same.
At Github I have a Fun with millis page. The examples "millis_soft_pulsating_led.ino" and "millis_led_heartbeat.ino" have a curve. Click on the blue text for the sketch, use the green button for the simulation in Wokwi.
I'm thinking about a random, going through a Gaussian curve, and then through a 10log curve for the human eye.