Due to my issues with klonopin I have spent hours researching this medication. It obviously affects everyone differently but I suspect your insomnia is due to the fact that the .125 mg is just not enough for you as your body became dependent on the medication at a higher dose. I assume you are on a slow taper which will be good long term. Just know (and you probably do) that the insomnia is a withdrawal side effect of this benzo and can persist for some time before it gets better. My primary doc (who couldn't believe my sleep doc gave me this junk) tried to put me on trazadone and to stop taking klonopin. Even the pharmacist said, you'll sleep like a baby! Nope, after stoping the klonopin was wide awake for it seemed weeks, the trazadone could not counter klonopin withdrawal effects.
Based upon my research on this drug, it affects all of us as it changes the makeup of our brain receptors, many people don't notice anything and it works fine for them, but make no mistake, it does alter our receptors and how our central nervous system works, mostly trying to calm it, i.e., anxiety control etc. The good news is that the changes to our brain etc. are NOT permanent once withdrawal begins but can last for extended periods of time for many. Some folks have no issues when withdrawing, mostly those who have properly tapered over time. I hate this drug and how it affected me, although I am much better now at almost 6 months cold turkey but still notice some side effects. I now sleep much better, although I still have nights, where an over the counter sleep aid helps. Best of luck to everyone here, just do what's right for you and you will overcome in time. You might find this piece on withdrawal symptoms helpful as well. God Bless you all!
https://www.benzoinfo.com/protracted-withdrawal-syndrome/