I just learned of this Forum and joined so please forgive me if I'm not going about this in the right way.
I have a 1990 Black Corvette Convertible that I have owned since new.
It has 60,000 miles, has always been stored in winter except for the last two years since I started wintering in Florida.
Last year I went to Ecklers and replaced the driver side headlamp motor and module, since then the headlamps no longer automatically activate when it gets dark, also if I start the engine first and turn on the lights they will not rotate. I have to turn off the engine, turn on the lights manually and they will rotate. Also I recently noticed that the passenger side running light was out. When I replaced the bulb with a 2057 lamp I noticed that when the running lghts are on the signal lights can not be seen although they are working faintly, also when I turn on the head lamps both the signal and running light filaments light up as though they are receiving to much voltage and they get very hot.
Welcome to the forum. I think you posted this in the wrong section. Better trying General Discussions or maybe Tech as you will get more responses there. This is the scan and tune section.
Perhaps the Canadian cars are different, but in the US, my 90 does not have auto lights on. I know there are aftermarket add-ons that will enable that feature.
I am wondering if the Canadian cars are different if the motor assembly might be different and the one you got from Eklers may be incompatible. Usually the motors need new plastic bushings to fix them. They are inexpensive ($5 or so) and can be installed with a little more work than removing the motor. I would check to see if the part numbers from your old motor is the same as the one Ekler's sent you.
As far as the other bulb issue, I wonder if you have a ground issue so it is not running enough current thru the bulb and so it is dim. Or perhaps the contacts are corroded.
However, the headlights should rotate engine on or off.