It’s not a clear cut issue.
I have experienced ABS lights continuously illuminated but extinguishing when the brake pedal is depressed ( which I assume to be normal)
With EBS sometimes the amber warning light will stay on, until the the vehicle reaches 5mph , then extinguishes ( again presumed normal)
The correct type of ABS lead is a factor, and it is important to establish whether you trailer is ABS or EBS equipped, as the operation differs
Usually if EBS is working correctly, their is virtually no delay in the application of the trailer brakes upon the brake pedal being pressed.
In such instances if there is a delay in operation or the brakes feel harder to apply than you would usually expect, suspect a problem