SC3coupe

iTrader: (4)

Where can I buy the 7 pin connector that plugs into the GX Under the rear bumper?

The car came with one sealed bag connector but it is not a Lexus one because it is just a rectangular one.
is that possibly a more common rectangular style that plugs in what you are trying to tow?

IndyGX

If I understand your question correctly, you have the 7 pin female plug outlet, and wondering where to buy the proper fitting? If that is what you are asking, it all depends on what you are towing. Some trailers have the 7 pin round male connector that will go right to that plug under your bumper for trailer lights to work.
If you have a trailer that uses the 4 pin rectangle plug, you can buy the adapter from AutoZone, Harbor Freight, probably amazon, and it will adapt from the 4 pin trailer plug to your 7 pin round plug under your bumper.