Why doesn't my flash fire from the hot shoe trigger?

I have a Yongnuo YN-560 III and a pair of RF-603II (C3) triggers. I have a Canon Rebel T5i.

I put one trigger on the hot shoe. When this trigger is in TX mode I get a blue comm light and I can fire a test flash using the large test button on the trigger. But when I press the shutter button to take a picture, there's no flash.

The trigger and flash are on Channel 1. The trigger on the hot shoe is set to TRX. TX is fine, TRX gives me no flash. The flash and camera are in M mode.

I don't have a trigger on the flash because the Mark III has a built-in trigger The problem seems to be the camera. The trigger can talk to the flash but the camera is not sending a flash command through the trigger in the hot shoe to the flash.

Grateful for anything you could suggest.