First off, welcome
The codes, yes they can be extracted by shorting two terminals on the OBD1 connector located about in the middle of the fusebox cover. It'* terminal A and B, which is the top two terminals.. just take a small piece of wire or anything conductive and connect the two. Then switch the ignition on and the SES light will flash the codes... and it'll flash one, two ..... one, two, three for a code 23. Then you go here
and then you know.
As far as the brake light indicator, that is normally due to corrosion on the bulb and socket. Remove all rear taillight/brake light/turnsignal/license plate light bulbs and thoroughly clean them for a good connection between the two. Otherwise I believe I remember there being a way to solder in a certain resistor and making the indicator go off... however it'* common for corrosion to cause the false bulb out indicator.