A couple more questions:
Is there a button on the back of the antenna ? Like a programing or valet button.....I can't tell from the pics
Where is the Ignition switch (key cylinder) in the dash or in the steering coloum ?
This box you found behind center console with the sticker on it, how many wires are coming off of it ?
I'm pretty sure your R/* is made by one of these 2 companies;
The antenna looks like it is a UltraStart antenna, but the remote looks like an Autostart (Command Start) remote.
I'm guessing but I still think that its a AutoStart product judging by the looks of the Remote.
FYI: AutoStart makes product under various names CommandStart (sold at BestBuy/Circuit City), ProStart, etc.
I have an idea that is kind of risky but might eventually happen anyways.
You could take apart the remote and see if there is a name stamped on the circuit board.
The risk involved with this is that the remote may no longer work if the battery is taken out or if it died. The remote may need to be reprogramed and without knowing what unit it is this would be difficult.
I would take the risk and see if there is a name on the circuit board. It'* either that or live with one remote until the battery dies, then see what happens after its replaced.
The only other way would be to find the R/* brain and look at it for markings. If you did this and took a pic of it, I would most likely be able to idenify it.
To do this remove underdash if necessary/possible, find the ignition harness and follow the wires coming off, of it to the brain.