2005 corolla vibration on turn signal on

[dpj52190]

I have a 05 corolla S with ~ 120k miles and when i'm at stop light(in drive but stopped) and turn signal on it get fluctuating vibrations. Its more noticeable at night when my head lights are on and turn signal is applied. I see a slight drop in rpm when the vibration occurs.
Also when the radiator fan is ON the rpm drops and the vibration is noticeable.
Fog lights ON has the vibration too.
I've changed spark plugs to OEM. Replaces serpentine belt(at home) OEM.
I've gotten the battery and alternator voltage checked at auto zone( car was in parked gear tho).
If in park and turn signal on, it doesn't vibrate. Even if the headlight or beam is on and signal light is applied it doesn't vibrate.

I am trying to pin point the problem and i've came up with some assumptions.
1st) since i changed the serpentine belt do I have to get the timing set again?
2nd) voltage regulator or slow reacting alternator.(or is there a rpm regulator screw that i can adjust)
3rd) since it only happens in drive and not in park or neutral it could also be related to transmission? I have to say that there is no noise or harsh shifting from the transmission.

No oil leaks, used synthetic oil every time.