I have a meticulously cared for 2003 Camry. When I got it a year ago it stalled at startup about 10% of the time, and it has increased to almost 50%. The engine light is on and off, but seems to have no bearing, nor does air or engine temperature. If I keep my foot on the gas even when stopped, I can drive it. Sometimes it warms up to idle, sometimes not. It stalls usually at start and always when going slow or stopping. Sometimes it succeeds in idling, sometimes it fails, but never something in between. Either it idles right at 1000rpm, or at 0.
Mechanic ran it through the computer, drove it around, tried it a bunch of times and found nothing.
Your 'engine light" is telling you that it’s storing fault codes.
The possible causes are myriad, and include a bad temp sensor, a bad fuel pump, badly eroded spark plugs, and a few other possibilities. A lot can be tested without having the fault happen. Perhaps a reputable shop with better diagnostic skills can help.
PostScript: if by “mechanic” you mean the dealer mechanic, don’t even bother going back. You need a reputable independently owned and operated shop. Dealers don’t want to be bothered with older cars.
My first guess would be dirty throttle body. Clean the throttle body. Before you do this please read the following as moving the throttle plate incorrectly could lead to a costly repair.
I would suspect a vacuum leak, dirty throttle body, or Idle Air Control valve problem. These can exist without leaving a code and the latter 2 can be directly related.