My guess is that neither of the triggers are working either. The 360 gamepad is not fully supported in GTA:SA.
However, an application is available that can get it to work. Try this:
http://www.pinnaclegameprofiler.com/forum/viewtopic.php?t=241

You'll need to register at that forum in order to download the files discussed in that thread.
The files that you download in that thread should be used with the application available from the main page of that website. The instructions in the thread should explain the rest.