Hi Robert,
Without your VIN I am just guessing you have a W-Series Workhorse chassis based on the part you are asking about. I don't think the two issues are related, but you can pretty easily remove the broken plastic threaded end of that switch from the master cylinder to install a replacement.
As for the rear brakes hanging up, where were the calipers purchased from? If you have installed calipers that are not from Workhorse then they do not have the correct bore diameter, and are known to do just what you are seeing.
The calipers for your chassis look just like other calipers you can buy, but the ones that you need were modified by Bosch for Workhorse so they wouldn't do that. Here is a link for the calipers you need https://www.workhorseparts.com/W8007383-W20-W22-Brake-Caliper-Asm-(66mm)
If you have already installed Workhorse calipers then I would look and see what side of the pads are hanging up. If it is the outside pads then make sure the guide pins are not tight in the bore and are well lubricated. If it is the inside pad, then I would attach a pressure gauge to the caliper and press and release the brake pedal a few times and see if it is dropping all the pressure when the brakes are released. If it is releasing all the pressure then you have a failed caliper, if it is not then it could be many things such as the master cylinder or brake booster and so on.
Hi David,
I would have that extracted, it is not too bad to get out since it is plastic. I have had good luck just driving a flat head screwdriver in there being careful of the threads in the master, then just turning it out of there. That switch warns you if your brake pedal is traveling too far, so you should have it operational.
That master switch is activated by a groove in the rod inside the master, when that groove lines up with the switch the brake failure light comes on with the buzzer (if the speaker is not blown) sometimes that rod gets stuck and you cannot unstick it so you have to replace the master cylinder
That groove lines up with the switch when the brake pedal goes down too far, like when you bleed the brakes