Okay, so the part above that I posted from advanced auto parts is the correct part and did solve my problem.
Now, for those who really want the meat of the solution. The proper name of the part/switch/relay is called a flasher unit (a.k.a. turn signal relay or hazard relay). I called the local advanced auto parts and asked if they knew where it went and sure enough, the place they mentioned, in the engine bay, was wrong. I posted up on their website asking for the location for my car (1993J) and the reply said the flasher unit is under the steering column on the right side.
So, I took off the housing underneath the steering column and sure enough, the part is there. It is very easy to replace and it takes only about 10 minutes to take off all of the screws, replace the switch and redo the screws.
Here is what the OEM part looks like:
http://www.courtesyparts.com/25710-flas ... ?cPath=882&
The aftermarket that I posted above is missing two things (which aren't important for a quick fix like this): the housing around the 3 pins so the clip and be OEM secured and the grooves for the unit to attach to the metal housing underneath the steering column.
Sorry for not taking any pictures, but it was getting dark out and the mosquitoes was biting my like crazy.
I hope this helps for anyone in the future.
The OEM replacement (from Infiniti of Scottsdale) is 30.00. The universal from Courtesy parts is 60.00. I purchased the aftermarket above for 12.99 + tax. No the aftermarket does not attach to the metal housing or does the clip snaps in place, but who cares for an 18 year old car that is car that keeps nickel and diming me.
Cheers and happy safe driving!!!