You might have a problem with the tranny or it's sensors. Seems funny, you say it only does this at night! WEIRD!!! This makes me wonder if it may be the ALT just like
sleeperrt said. Which would explain why the lights flicker. If the ALT is not putting out enough amps to supply the car with enough juice it could also cause this. However I have run my car off of just the battery and I had no real problems with driveability until my lights dimmed, guages went nuts and I lost all juice. It ran just fine up till it died from lack of battery power. So it may not be the Alt. To have it tested run down to the local autozone or advanced auto and they will test it for free.
Do the ATX's have a stall converter or something like that inside the tranny? That would be another instant guess that Id start with. Maybe the tranny is not wanting to free wheel while you are stopped. Kinda like an MTX dies when you forget to push in the clutch. Good luck man!
The lights are probably flickering because the idle is going so low. The only trans sensor that affects idle is speed sensor regardless of trans (3 speed or 4). If the speedo is operating normally the speed sensor is working properly. need more info. what year car, milage, last tune-up. could still be the battery even though the alt is o.k. may need to take to a good technician for proper diagnostics.