HVAC blower stopped working

My vehicle listed above Alpha's HVAC blower stopped working one hot afternoon while running on high for sometime.

Did all usual suspected checks, found the blower resistor connector was burnt, but had been previously repaired by splicing a wire in place of the burnt terminal and solder.
I've replaced the connector and resistor now that I've had it off.

Still no fix. While on the highest setting, can hear the relay buzzing, turning on and off rapidly.
I did remove the blower and connected directly to battery, it works fine.
Another odd thing that happens when trying to turn on the blower, the wiper comes on and sometimes I get "Traction Failed' on the dash.

Not sure if it's related, but I have an issue with my right turn signal as well. Selecting right, turn on the left turn signal. Sometimes its flickers on and off, sometimes it's okay if I choose left then right (but can see the left momentarily flash once even when selecting right).