Quite a simple 1 i think. Remove your rear light fittings - the bit the bulbs go in - you will probably find that either the bulb holders/plugs are soaking wet and maybe a build up of a green coloured sludge. Clean this off (scrape/small wire brush) then spray plenty of WD40 about the area. You may find the terminals are completely rotten in which case replacement holders will be in order. Another probably easier to check will be to make sure you actually have the correct bulbs in place. What is happening is that there is a live feed returning to your fuse box wihen you apply the brakes which is coming from your side light circuit hence the engine running on etc.
Joe (Inverclyde/Strathclyde), February 2009