I'm having trouble adjusting the parking brake to hold the car. Is it possible the toggles on the rear calipers where the cables attach can become rusted?

 

Certainly possible,especially if regular brake fluid flushing wasn't performed.
Mark the toggles with a marker an see if they both move after applying the brake.

 

One or both of your rear caliper pistons could also be seized. Happened on my R53. Rebuilt the caliper and the parking brake works perfectly.

 

Here are the cables and you can lube them, for example on the Gen 1 MINIs

https://www.northamericanmotoring.co...ake-lever.html

https://www.northamericanmotoring.co...more-http.html

My caliper seized and i got new ones, the MINI life of a almost 300K car. The ohio salt kills them. 34216763729 34216763730 We just landed the 4/2003+ in bemmen parts. I did one side and then down the road the other one went. Got new and all better. Most of the time you can reuse the carrier.




On the gen 2 R56 ( your MINI ) we are seeing the same thing. Cables need replaced and the calipers. You can lube them under the boots to buy some time.

https://www.ecstuning.com/Search/SiteSearch/3440676995/

Rear calipers: https://www.ecstuning.com/Search/Sit...h/34216785611/
https://www.ecstuning.com/Search/Sit...h/34216785612/