Breaking makes rear lights go out ???

Check for a bad bulb. This is a normal thing. I'd bet your right stoplight is out.

Gerard

Your bulb is bad, or there is corrosion preventing a proper ground.

It's probably a dual-filament bulb. Normally, one end of each filament connects to a pair of contacts. The other ends of the filaments are tied together and go to ground or similar.

When the driving lights are off, does the brake light work properly?

What's happening is that, with just the driving lights on, the low- wattage filament is getting power from it's contact, but the current can't flow back to ground. Instead, it's flowing through the high-wattage (brake light) filament, which is probably at ground when off. Another possibility is that it has a poor ground connection, which allows enough current for the driving light, but not the brake light.

When you hit the brakes, both contacts are positive, so current cannot flow.

I would first remove the bulb and check for corrosion, cleaning if necessary. Depending on how hard it is to get at, it may help to simply replace the bulb while you are at it anyways.

bad ground

bad connections, as most people here have suggested, it was a common problem with escorts in the UK, i'm not sure if the same bulb housing was used in canada but either way it will be the earth (ground) on the rear light cluster causing your problem.

Neat. Well, to me it is. Friends of mine have an almost identical Escort (early 90's but I don't know the exact year or engine size) here in the US. They have the exact same problem with the exact same light bulb. At least you can take consolation in knowing it isn't just you ;-). With the explanations given to you, maybe we can now fix their car :-).