This is a really long shot, but I'm going to take another guess:
The task your boss gave you is to take home (or steal) a radioactive substance of some kind! Uranium perhaps?
Inside my lunchbox
My charge goes every night,
Stored in my cupboard
Until brought back first light.
This paragraph makes more sense when coupled with the proceeding paragraph. It sounds like you are smuggling home the uranium in your lunchbox. You store it in your cupboard - or perhaps this is code for a nuclear reactor. (Perhaps by morning, it is glowing? Lol - not sure about this.)
You see, boss gave me a task
That’s to be done every day.
I take Tea home on Wednesday,
But it’s Thirsty by Friday.
There is a Foyle's War episode where a scientist steals radioactive uranium samples from a company by smuggling it in his tea flask (hence the capitalisation of "Tea" perhaps?). Only you choose to use a lunchbox. The reference to being thirsty may be because you are building a nuclear reactor (or selling it to someone who has one), hence the constant need for water to cool the core...
You’ll have to buy fresh
If you play this for keeps.
When they do this with your food,
You won’t hear any beeps.
Newly enriched ("fresh") uranium is more valuable than depleted uranium. Unlike a microwave (which beeps when finished), you won't hear any beeps if you used this to cook your food.
I set things up myself.
It wasn’t a huge bother.
The rest just sit on a shelf
As they wait for their brother.
I'm not sure about this last paragraph. Maybe "the rest" refers to other rods in the reactor core ("a shelf") and their "brother" is the rest of the system/computer terminal?
The thing that I care for
Works best in a set.
If you’re into this puzzle,
What you hear’s what you get.
Obviously you'll need more than 1 rod or more than 1 uranium sample to be effective. The last line doesn't really fit though.
Sorry, I have no idea how hint 2 applies.