I flushed and changed my coolant not too long ago, and after I filled everything up (including the overflow bottle) my "birdcage" light was still on. It turns out that when I was shooting a high pressure stream of water in the bottle to clean out all the goopies, I cause the float on the sensor to get stuck. I took the bottle back out, dumped it out and turned the whole thing over and the float didnt move. I gently reached inside with a screwdriver and free'd it up. That cured that issue.
If your check brake light warning is coming on and going off it sounds to me like you may have a bad connection somewhere. I have seen bulbs get all corroded and make poor contact in their sockets lots of times. I would start there. Take each of the bulbs out, clean them (one of those green kitchen scrubbers works great for this) and put them back in.
As for your check engine light being on, it means that your computer has senced something is wrong or was wrong in at least one area of operation of the engine/trans. It could be simple or it could be real trouble. you wont knonw until you "retrieve" the code from the memory.
Go to this page to understand more about checking your codes:
http://www.toyota-supra.info/forums/...read.php?t=323