Have you checked the auto power-off setting on the secondary camera (the T5i)?

When my Rebel T7 turns off after the timeout, it takes a second or two for it to "wake up" when I half-press the shutter (or press any other button). If the camera is in auto-off and I fully depress the shutter without waiting for it to wake up, it does not take a photo. I suspect this is what's happening with your remote trigger -- it attempts to fire the shutter immediately upon receiving the signal, but since the camera is in auto-off, it isn't able to take the photo.

On my camera, this setting is labelled "Auto power off" and is found under the first yellow wrench of the settings menu. Try setting it to "Disable".

Note that this will likely impact your battery life. Since you're intending to operate the camera remotely, you can adjust other options to conserve battery, such as turning off the display and disabling image review.

As a side note, you may want to cover the eyepiece on the secondary camera, since light entering through the viewfinder can affect the light meter and confuse the auto exposure. Ordinarily your face is there to block the light, but since you're across the field you'll need to use something else :) The neck strap of my T7 came with a little rubber piece that's designed to cover the eyepiece in this type of situation. This Canon page describes how to remove the eyecup and attach the eyepiece cover.