OK, the most important part is the cable fitment and alignment to the instrument. That square port should be clean all the way to its bottom, so the cable doesn't apply linear pressure or angular pressure. If you are working with the OEM cable, that square end can become slightly distorted or less than exactly square. It doesn't hurt to kiss it lightly with a fine file to get it closer to square. I have rotated them 90 degrees to find the best fit in a port that is also worn with age.
And about the dash illumination bulbs (4 of supplied by an orange wire), they operate through a dimming rheostat so there is going to be some voltage drop found there. And slightly above 13 volts is not a problem. Voltage regulator should allow 13.2 or so. Run the vehicle and maintain battery to just above 12 volts.