So this what the throttle cable exit at my firewall looks like. That can't be right. The tube is not attached to the firewall, and the threaded end of the cable wouldn't slide out. The string in the picture was used to pull the cable perpendicular to the firewall. Needless to say, this wasn't working very well.

What should this look like? What do I need to do?

Click to view attachment

Here ya go.
Mike

It looks like the tail-end of the throttle cable tube broke off. The easiest thing would be to remove the cable, find the end piece in the cable sheath and weld it back on.

looks like someone may have tried to fix that once before. Here is a pic from a thread about the clutch tube repair that has to be done quite often on these cars.

Click to view attachment

Hope this helps with your initial question. Do a search for clutch tube repairs and you will find lots of photos of the area in question. Someone will chime in who has actually repaired the throttle cable tube i am sure.

Jim

get thee to a welding shop!. The clutch tube broke badly years ago and someone improperly rigged it affecting the accelerator cable tube. The fix is relatively easy