Yes the Hopkins Active Tail Light Converter with Install Kit # 46255 you were looking at is confirmed to fit your 2003 Lexus GS 300 and will work perfectly to give you a fully functional 4-way connector.
Since this harness and all of the other harness are splice in harness, you will want to use circuit tester # PTW2993 to find the correct wires on your vehicle.
If you do not already have a trailer hitch receiver I recommend going with the Curt Trailer Hitch Receiver - Custom Fit - Class... view full answer...
Since you didn't give me the years of your vehicles I can tell you that the Hollywood Trunk Rack part # HRF2 can fit 2004-2006 Lexus RX 330 and 1994-2006 Lexus GS 300. I attached a review video for you to check out as well.
If you plan on carrying any womens or alternative framed bikes without horizontal top tubes you may also be interested in purchasing a Swagman Easy-Out Women's and Alternative Frame Bike Adapter # 64005 to provide a horizontal top tube on your bikes to provide an attachment... view full answer...
The Curt Trailer Hitch Receiver - Multi Fit - Class III - 2", part # C13900 does not work with your vehicle. However the Curt Trailer Hitch Receiver - Custom Fit - Class I - 1-1/4", part # C11372 will work with your vehicle. It is a Class I hitch receiver with maximum tongue weight of 200lbs. I have included a product link below as well as an installation video. view full answer...