Sound like a tube is burnt out(not common but does happen) the transformer i figure would work or not work, not just work on one side and not the other. You could get a neon sign place to make you a new tube, you'd have to break open the case and bring them one to match, should only cost at most 40.00. while you are in there i'd move the exsiting transformer to the outside of the unit, because those go more often and getting into the housing is a pain, if you ever have to replace that too.
There is one in the classified right now for sale, 125.00. sounds like a good deal to me, then you'd have extra parts if some thing goes wrong with the other one.
Here's my link to the fix
http://www.cadillacforums.com/forums...ix-redeux.html