There is a "sweet spot" in the switch on my '90 Mustang. If I don't get it in the right spot the taillights and smaller lights in the front wont work. I replaced the switch and it still does the same thing. The pigtail doesn't look burnt or bad. All the wires seem snug into the connector.
Could be a bad swtich. With the pigtail pulled out of the gauge cluster and the switch connected heck the power and negative wire for the tails coming off the switch, then check the ground wires in the rear.
Does the switch or gauge cluster feel warm when the lights are on?