Parking brake is integrated into rear caliper. Check pads and calipers for proper FUNCTION - BEFORE making any adjustments.- Generally, barring mechanical fault(s) , that type is self-adjusting with normal use.
I also have a 2006 since she had 5 whole miles on her. We've had alot of issues, so if it can happen to a Solstice, I've probably had it happen. In this case, sadly if you have had the Ebrake adjusted and it still does nothing, it's probably an issue with the calipers. Apparently our E-brake is tied into that system. I know remanufactured sets are about $500+. I have had 3 different garages tell me this is the problem as i refused to accept it from the first. Anyway, I have since also read on the solstice forum a potential fix by readjusting the pistons? I'm at that phase, I have a garage investigating that before we do another $1000 of work. I've copied and pasted this from the forum, it didn't mean much to me, but seemed to work for several.... "NOTE: If adjusted the park brake cable as far as it will go but can't get the brake to hold. The rear brake pads are good (have plenty of pad left) and the brake cable is operating the lever on the rear calipers. Then remove the rear calipers, collapsed the rear calipers buy screwing the pistons in (just like you would do if you were doing a brake job) then install the calipers. Using the brake pedal pump the brakes back up (usually takes 5-8 pumps) then test the park brake. "