Scotty I have a JDM 1993 Toyota Corolla LXi Limited with a 1.6 liter 4 and a 5 speed manual. it is all wheel drive. with a rediculous low 3000 km on the clock I imported a while back. runs great. needed a new battery and the battery size is like a prius size battery. I went to autoparts store to buy replacement battery and told them 1993 Toyota corolla and specified it was JDM. the store clerk said these are all the same and the battery was bigger than the original and barely fit snugged in its compartment. I couldn't use the holding bracket and I had order an SAE to Pencil post adapter which was like $17 on Amazon and fired up fine, also did oil change and filter as who knows how long this car sat as well as new tires. my concern is if the wrong size makes a difference as the type is from what i gathered is H4. the rear brake lights stay on and I thought either electrical or grounding issue. it did not do this before. this Corolla does not have power anything except for the steering and brakes and the AWD button to switch between front to AWD. I tried searching online for that specific battery made for the JDM Corolla model AE104. any help greatly appreciated.
And what about the brakes lights staying on
probably a faulty brake switch
I had the "brake lights stay on" problem on a 93 MR2 - it was a Brake Light Stop Pad - here is a link on the issue, which very well could be your problem
"The brake pedal stop pad, or brake light stop pad, is a small stopper that pushes in the brake light switch to turn off your brake lights when the brake pedal is not depressed. It is found attached to the brake pedal arm under the dashboard. It is usually made of plastic and can wear out over time. If you notice plastic pieces on your floorboard and your brake lights stay on when the brake pedal is not depressed, you may need a new brake pedal stop pad or brake light switch."
https://www.toyotanation.com/threads/brake-light-switch-and-brake-pedal-stop.551250/
BTW I have found the Toyotanation forum to be very helpful, especially for less common models/problems.
As long as it fits and starts every time, I wouldn’t worry about it.
And what about the brakes lights staying on when I shut car off? I do unplug it when not driving it.