Ford \focus 1999 dual filament rear light not working, works fine when braking

Replace the right rear brake light bulb. It is possible that the filament has burnt out and has fallen across to rest on the brake light filament. This would cause the condition you are experiencing.

Blown fuse ,bad headlight switch,or wiring issue.
the tail lights have there own fuse and are powered through headlight switch. Do the front running lights come on? If none of them work, switch could be bad if front work and rears dont, check bulbs and power to them when lights are on

is it just the brake lights or the tail lights when the headlights are on? the tail lights may have a double filament bulb one lights up when brake is applied and the other filament is for just tail lihts so check the bulbs carefully and if you see one filament is broken replace the bulb. also make sure the socket where the bulb seats is not corroded or dirty

The turn signals and brake lights use the same circuit and filament in the bulbs. The tail lights are on the other circuit which comes from the headlight switch.
Do you have power on the tail light fuse ?

brake and turn are the same filament in the bulb. Try a new bulb. if that doesn't work your going to chase a short/ground on that wire back to the switch. get a wiring diagram to help.

The brake light side of the bulbs is powered by the brake switch and travels thru the turn signal switch.
If the third brake light works, I would guess the problem is in the turn signal switch.

there must be a short circuit which powers tail lights and brake lights. probably you have a dual filament bulbs which have both brake and tail light together. check for bulb, socket/or bulb housing and harness of that light.

Broken wire where trunk lid opens

The outer lights are dual filament bulbs, meaning they work 2 separate functions, brake and running lights. Either filament can burn out separate from the other, thus creating the situation you have. Replace the bulbs and your problem should be fixed.

The tail lights working would not necessarily mean that the brake light bulbs are good. If they are the type that have a double filament (ie: one filament for the tail light and another filament for the brake light ) the brake light filament could be bad and the tail lights still would work. If they are either single filament type bulbs or double filament type, I would check the bulb, fuses, and contact switch on the brake pedal.