The bleeders on the ATE rear calipers are on the bottom.
New brake lines have been ordered. The old ones are not kinked.
The brake pedal is firm when pressed. The front brakes work fine.
I allowed each caliper (one at a time) to drip bleed about 20 minutes each last night and I did not test the rear brakes yet.
How should I diagnos a malfunctioning master cylinder?

I thought that might be the case. It's hard to bleed the air out of the caliper with the valves on the bottom.

Typically, a leaking m/c will allow the brake pedal to go the the floor if pressure is applied continuously.