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Both the left brake, and the right brake, are controlled by the same brake valve, so if only one is locking up, I suspect a problem with the brake in that motor.
Test the pressure on the line supplying that brake. There should be 400-420 psi at high idle.
Use a port-a-power to pressure test the brake in the motor to see if it is leaking. Pump it up to about 450 psi and it should hold pressure. If not, the brake piston is leaking.
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There is no way to bypass the brake system, and I wouldn't advise doing something as unsafe as that if there was.
Each motor has a park brake that is spring applied, and uses pressure to release. What were the pressure testing results for each motor brake?
Are you sure the problem is the brake, or is it a problem with the motor or the hydrostatic pump for that side? Tee a gauge in with the motor brake line. Is pressure always available to the brake while running the travel functions?