If you have patience, you don't need any additional equipment.
I couldn't agree more. People just want to rush things and add unnecessary catalysts.
The key is to do it slow.
1. No catalysts of any kind! This includes laundry boosters and bleach.
2. Room temperature only! Warming (or heating) the peroxide bath speeds things up but also causes too much oxygen release at once that damages the plastic. Heat it too much and the plastic will melt.
3. It's pointless to use too strong peroxyde solution. 15% is more than enough.
4. Peroxyde decomposition is a very slow proccess so a peroxide bath can be reused many times as long as it's clean.
5. Using an UV lamp or exposing the peroxide bath to direct sunlight is unnecessary. Placing the container next to the window is more than enough.
6. Cover the container but don't make it airtight. Allow the excess oxygen to escape.
7. Use rubber gloves at all times. If you get peroxide on a wound you will understand what real pain is.
8. Patience! Good results take time.
+1: Some plastics won't brighten at all no matter what.
You don't have to worry about the plastic getting brittle after 20 years. I rearticulate animal bones as a hobby and it is the same proccess. This cat was my first project 15 years ago and it's in very good shape, no change in the bone structure at all. Beautiful as ever.
I brightened a piece of 5.25 bay cover today to demonstrate the effectiveness of this method.
It was placed in a 15% cold H2O2 solution and put in the window, not exposed to direct sunlight at all. It took exactly 12 hours to achieve this level of brightness (compared to the other cover I didn't brighten). You can do it in the basement if you like, it just takes longer.