99 mercury mystide had rear running light broken

not sure if this link will help you find out but have a look.
What kind of straps are under 1999 mercury cougar rear passenger seat...

you can buy the filler part for that 99 mercury mystique

Fuel Tank Filler Neck

depends on shop rate and how much damage is done to the right side of the car and what is damaged.

I have a 99. On my car, there is a small notch in the center console cover on the bottom right, just by the front of the passenger seat. Stick a screwdriver in there and move the point backwards to trip the release.

HI Matt,
Your issue sounds like a fault, most likely in the rear lights. Current is feeding from the brake light circuit, into the running light circuit. The most common causes are a bulb filament broken and touching the running light circuit, and loss of ground.
observe the rear lights closely and you should get a clue as to which light is failing....but if not, just pick one....
I would run a temporary ground and test again, if no results, pull the brake light bulbs...
Transient current is often difficult to wrap your mind around, until you understand what can happen.
Doc

It uses an 1156.

it is the alternator.
and also check the 175amp ford fuse stuck to the firewall passenger side on the wire connected to the alternator and the starter. same engine as the 99 cougar.

Check the brake light fuse. The high mounted brake light (third brake light) is on a different circuit than the brake lights. Hope this helps.

That's the rear foglight socket. The rear foglight idea is European, and they ship the Audi over with a rear foglight as well, but it's only on the driver's side (that's the way rear fogs are done in Europe). That socket is fully powered though, and wired to the same dash switch as the driver's side rear fog. What you can do (what I did on my 99 A4) was to use a drill and **** out the rectangular opening in the rear taillight panel, and then put a bulb in that socket. Voila, instant dual rear fogs.

This is a good idea because in Europe, the police understand that a rear fog is only on one side. In the US, our police don't always know that, and you may get pulled over if you have that on - they may think you have a blown taillight bulb. Do the dual fog mod as described above - it'll save you the hassle and it looks better too.