I am glad he is better. For 2.5 gall actually you always need to do 1-50 and 1-100% water changes a week. Some people even recommend 2-50% and 1-100% a week.
If you would have light 24/7 it will definitely stress him out.
I am confused that you wrote taht he has that with goldy sheen cover or color on him when you shine the light. Is it something new or he was like that when you bought him?
The reason why i recommended to raise the temp because temperature over 85* will help to speed up parasites (velvet)life cycle and they will fall faster and some even said that temp over 85* will even kill them. So i am wondering if he really has velvet and the water changes and temp raised helped.
Temp 76* will never make betta lethargic. So the fact that he was lethargic means that something was wrong. Usually bettas pretty active not laying on the bottom. My bettas actually live in 76* and some even in 74*. So really it not the temp that made him lethargic before.
So if that color that you talking about is new and i actually can not see it on the picture what i would do is raise the temperature as much as you can and do aquarium salt with daily 100% water changes.
Just like Sakura wrote : ''The salt will help balance his electrolyte level and encourage the production of slime coat, which will in turn help protect him from infection and infestation of parasites''.
And if that color you talking about is new then i would even increase the aq salt dose up to 2 tsp/gall with daily water changes. Unless it just his natural color and he had it before then just water changes will help.