check out this page
http://www.clublexus.com/forums/lexus-audio-video-security-and-electronics/269156-how-to-build-and-hardwire-an-auxillary-input-to-oem-stereo.html
could it be your alternator, these are common parts to fail and as i understand the extra drain from the brake lights etc can cause car to stall if alternator is not working. Sorry not more informative.
