Fwiw, your battery is toast if it's 10 years old.
You checked, you have a 12v available lamp lit.
To check the brake you have to pull out the lanyard (well, the pin) on the switch mounted to the tongue. It's a good thing to test in any case.
It may break. They can be bought at a lot of places. Iirc, there may be more than one type. Fairly easy to replace the switch if you have to.
Then (working battery, pin removed and switch closed) pull the truck forward. The brakes should come on.
They will be at 100%. Do this on softer ground and have a helper note which wheels lock up (or, don't lock up).