This Tow Ready Custom Fit Vehicle Wiring, # 118360, would be the correct wiring kit for your 1999 Isuzu Amigo. Most likely the 5x8 utility trailer that you are renting will have a 4-way connector that will plug right into the 4-way trailer connector from the # 118360.
I attached installation instructions for this product for you to check out also.
You may also be interested in the following products to complete your tow setup:
Curt Trailer Hitch # C13235
Class II Drawbar # 36053
Hitch... view full answer...
For your 1998 Isuzu Amigo you'll first need a trailer hitch that is rated for weight distribution. For that the Curt part # C13235 is a great choice. Then you can use a weight distribution system like the Blue Ox kit part # BLU45FR which has a tongue weight range of up to 550 lbs.
For a 2-5/16 inch ball # 19286.
For trailer wiring you'd then want the Hopkins kit part # HM43215. view full answer...
To install the Carr Deluxe Light Mounting Bar # CARR210341 that you referenced on your 1994 Isuzu Amigo, you will just need the Gutterless Mount Kit # CARR220051. This bracket is confirmed to fit your vehicle and will allow you to mount the light mounting bar with ease. Its custom design will ensure a precise fit and all the needed hardware is included.
I have attached the installation instructions that you can also check out. view full answer...