Then the question remains, how would one traveling at the speed of light determine anything to not be "at rest" without a time delta?
Not quite right, I'm afraid.
If you and I are traveling at the speed of light relative to each other - I appear to you as not aging and you appear to me as not aging -hence the twin paradox. Neither of us is right or wrong nor our observations true or false. Since there is no absolute frame of reference neither of us can be said to be ACTUALLLY traveling at the speed of light - only the there is a relative speed between us - I claim you are while you claim I am.
So both of us 'experience' time 'normally' but 'observe' the other to not be.