My wifes 98 Lumina's passenger side(right) brake light goes out when using the driver side(left) turn signal. I have been told this could be a grounding issue but i have no idea where to start looking. Any information would be appreciated.

 

99% of the time this is a ground issue in the socket. Replace the socket, half of the time you can not see anything wrong with it.

 

try pulling back on the turn signal switch lever, there is a flaw in the turn signal switch of the lumina and monte carlo, my car did this also, i have a 98 monte and i had to pull back on the lever to get the brake lights to work.

 

sounds like a bad turn signal switch i had the same problem with mind replacing the turn signal switch fixed it.this is a common problem with the w-body vehicles.