On left turn the signal switch does not return to neutral

Try an put the gear selector in neutral , could be a park neutral safety switch problem . If that doesn't do it ,maybe the starter relay .Do you know how to test electrical circuits with a voltmeter ? Voltage drop test the starter main battery cable .
Starter Voltage Drop

Transmission range sensor , through electrical signals to the PCM ,it knows what gear the vehicle is in . Some all so call it a Park neutral switch , but it does more then that . The park neutral part of it won't allow the vehicle to start unless it is in park or neutral .

check the fuses, if that is not the cause, check the voltage at the bulb socket. If the voltage is ok, you have a bad ground. If there is no voltage, check the flasher and if that is ok, check the turn switch.

to fix the clicking noise, replace the hazard switch.
Turn Signals Problems on Malibu Impala Alero Cutlass Grand Am Monte Carlo...

The first thing is to replace the flasher, the 4ways and signals use diffrent flashers, after replacing the flasher or changing it with the 4way flasher and see what happens. if this doesnt help then you may have a bad signal switch, a good trick is to turn on the signal and watch it as you move the lever around, pull back a little or lift it more and pull down a little, sometimes the switch contact goes bad and by moving the lever without take signal off will make it flash and if that happens then the signal switch is bad even if the 4ways work this still means a bad switch, the 4ways are wired through diffrent contacts then each signal, good luck.

if you mean they won't shut off after you complete the turn you may have a broken turn signal switch or a broken spring in the switch BUT you can't get just the spring

Hi you may have a poor earth connection to the lights or a wire from the lights is touching the car body or another wire.

Was the relay switch new that you replaced? the one behind the dash?

Regards
Dan

the ac computer is on the fritz or the ac control panel has a short in it

remove the cover and you will see the bolts holding it on.some times you have to remove the steering wheel.you have to disconect the wire harness as well.

If the left side still works, its not the blinker relay, the thing you hear ticking. Both left and right signals go through the same signal stat. Turn on your hazard flashers and make sure the bulbs on both the left and right side come on. If the do, you may have a problem with the turn signal switch on the steering column itself. If only the left comes on, it could be bad bulbs on the right side or a wiring issue. Wiring issues are more rare on Park Aves.