When I write something that an object, like a clock, says should it be as though I was referring to a character talking (e.g. The clock read "1:13") or without the quotation marks? Thank you!
It depends on message from the object. If, like a clock, it is simply showing some information, then quotes don't fit the need. To use your clock example,
The blinding red digits on the alarm clock said it was 4:13 AM. Time to catch a quick nap before the daylight, and the next attack.
If the clock were more of an anthropomorphic character:
The blinding red digits burned forth from my aging alarm clock. The dial showed 4:13 AM, but the clock shouted to me, "Again, you have no time to sleep! Again! When will this change?"