Looks like the Body Control Module under the dash that controls all light bulbs is damaged.

The OEM Celica tail/brake light is dual filament incandescent 7440.

I replaced them with a LED bulb in the original socket, bought from China via eBay. One is fine, one bulb's wire got hot and burned, melted the socket. It did not blow the fuse and worked well for a couple years. One License Plate wire had cracks along 6 inch length.

Eventually I had a short somewhere, tail light fuse blew. A craigslist guy wanted $150 diagnostics then more for repairs. I did not want to spend that money, guessing the shorts are easy to find, went in trouble shooting, replacing the 7.5 A with a 30A so the bulbs stay on long enough for me to find the short, but it overheated, burned and melted the fuse panel, blew the Body Control Module which costs $1,100 at dealer. Most other light bulbs and body functions went kaput, only front head lights and power windows were working. I spent lots of time in many days trying to find and fix the problem to no avail, causing more serious damages. Damn stupid. I was able to buy an used BCM/Fuse panel in eBay for $70.

I suspected a branch of wire harness was shorting inside the hatch's channel, was about to cut wires, pull it out and check for shorts, finally I wised up that I had no tools, did not know how to remove the rear defrosters' terminals without breaking. I called my trusty mechanics, he referred me to a local chassis electrical guy. He said $95 to find and fix the short. He installed the new BCM, things started working again. He looked at the tail light wiring and took out all body plastic panels, found the tail light wire had insulation completely melted along the whole length and a burned out spot behind the panel at the left passenger side. The guy who installed the digital video camera took that panel out and could likely have pinched the wire against the chassis, but that wire is also in the middle of the harness, so who knows.

Repair guy found the tail light wire got hot enough to melt and burn off insulation all along its length. He also found the License Plate bulb's insulation brittled, cracked and open in a length about 6 ", could only be caused by heat. This tiny LED bulb supposedly draws very little DC current. I cannot explain why it got so hot. He had to unbundle the wire harness and run a long replacement wire from the burn spot to the fuse box under the dash. He said he found lots of problems with LED bulbs. He repaired thousands cars and should better than I. He replaced all rear light bulbs with incandescent. I paid him $200 total for the extra work. This guy is good and honest, recommended.

Any bros has bette rundersatanding of this LED problem, would be interesting to know.