the clock in Bad Cooper's car
Yes, it was 2.53. The exact time Dougie swapped places with Cooper.
"2 5 3. Time and time again."
It's not what the arm was referencing, in the sense that it was talking about the swap, and yet it is, as it specifically explains that it will happen again and again:
253 when Coop leaves (253)
253 on Oct 1st. (time..)
253 on Oct 2nd. (... and time again).
FIRE TWERK WITH ME