If the cargo carrier and the cargo loaded on it do not obscure the vehicle tail lights, you do not have to have a light kit installed on the carrier. However, it is still a good idea to get a light kit for safety purposes. Since you have the wagon model of the 1995 Buick Roadmaster, you would first need to install Tow Ready Custom Fit Vehicle Wiring, # C55352.
For cargo carrier, # 63155, you can use light kit # 20174. I have included a link to the installation details for the vehicle wiring... view full answer...
The only trailer hitch receiver that is available for your 1993 Buick Roadmaster Sedan is the Curt Trailer Hitch Receiver # C12009. It is a Class II hitch with a 1-1/4" receiver as you mentioned. It has a Gross Trailer Weight (GTW) of 3,500 lbs and a Tongue Weight (TW) of 350 lbs.
If your Roadmaster and this trailer hitch are rated high enough for your trailer then you will just need Trailer Wiring # HM11141185 and a compatible ball mount and hitch ball. The Curt Towing Starter Kit # C45147... view full answer...