No rear brakes and handbrake all the way up

If you have a handbrake, you can remove some screws around the handbrake covering. The screws are sometimes well hidden so you have to look around.
When you get the covering off, there are two adjusting nuts at the rear of the handbrake. Turn the nuts until you can get "5 clicks" on the handbrake to set the brakes.
Some jack up the car while doing this so they can rotate the wheels by hand to feel when the brakes touch the pads.
Hope this helps

Make sure your handbrake cable is adjusted properly. Adjust the rear brake shoes down to where the wheels turn freely with the linings only just touching the drums. Be sure to pump the pedal a few times after adjusting, then try again.
The front wheels (pads and calipers) will just about never bind, so concentrate on the rear wheels. If you do suspect the front wheels, release the bleeder valve for just a second and then try again.

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piece of cake ,the pistons just push in front and rear ,the handbrake is inside the rear brake disk so dont forget to strip and lubrcate the operating mechanisms for the handbrake with some nice copperslip in the adjuster .Also most important is to polish it every week and clean seats with leather restorer every month after all it is a real car as its a JAGUAR

car has 4 wheel disc brakes take off the rear pads and rotors u will see a set of shoes on the inside of that adjust thiem up and u should get alot more hand brake

he lied or the other brake cable also require a change
it is also posable that th rear brakes are not engaging

to test brakes
go to underground concrete parking lot must be smooth concrete and best place to find it is in undergrounds

acelerate in a strait line to 20 mph or 20 km
slam the brake pedal to thew floor causing a skid pump brakes if you have abs
now get out and check all 4 tires have skid patches
if not go in reverst to 10 mph and hit the brakes hard
let it slide
now get out and check skid marks
if you dont get skid marks front and rear it is time to talk to your mechanic
as for brake cables there are usually 3 of them
1 from hand controll then 1 for eash rear wheel somtimes they are on axcell and somtimes they run direct across the trailing arms

Maybe, but probably not. If all those things were messed up, you'd also have trouble with the brakes under normal driving conditions.

You don't need a Mazda mechanic to work on your brakes, but you should find another garage and at least get a second opinion.

Miata brakes are very easy to work on -- not much harder than changing a tire. If you're up for it, get a Chilton's or Haynes manual from your local library or auto parts place and dive in. It's straightforward to inspect them yourself, and even replace your own pads with simple tools.

sounds like brake pad sensor damaged or did you forget to put in new pads or removed? if its got one.
low fluid in brake reservoir can cause light to stay on also
or hand brake light switch shorted to earth have seen coins jammed in there b4

Chalk the front wheels, car is on jackstands i hope, release the handbrake, use the old pad with a c- clamp to compress the pistion on the caliper, install new pads. may have to take the cap off the master cylinder, if none of this works, open the bleeder valve, and compress the piston, rebleed the caliper.

The tightness of the handbrake is a function of the adjustmnent of the rear brakes. If the rear brakes are working properly, the handbrake adjustment will be correct. I would change the rear brake pads first, before I tried anything else. Worn pads or nonfunctioning adjusters are the likely culprit.
If you do not want to repalce the rear brakes, you can find the instructions for tightening the handbrake on a website called Focushacks.com. But, if you make the modification (I don't recommend it) you will have to change it back when you get around to changing the rear pads.