The only thing you could do would be to take out the dimmer and install a normal switch

Halogens get very hot. Wiggling the lampholder suggests that heat damage has occurred and poor contact is the result. At this point, every component of that fixture is a suspect.

So after more troubleshooting it looks like the lampholder and transformer are shot on the original bad side. The other light works again after changing the bulb. Can I assume that all the wiring is fine and all I need to do is replace the bad lampholder and transformer? Thank you in advance.

So I'm trying to replace the lamp holder. After stripping the wire to attach it to the new lamp holder, I see the color of the wire is dark instead of silver. Does this mean that that wire is bad and needs to be replaced?