Picked up a 98 accord and none of the rear light that would be on without hitting the brakes are on. I would assume it'd be related to the daytime running light system. Not being too well versed in the electrical side of things I don't want to dig into it without a solid lead on where I should look first. Fuses for all of the lights aren't blown, but my dash cluster lights don't work either.
Note: the brake lights work when the brake light switch is activated as it should. but nothing when the car is running at night.

 

IDK that I can help at all but, are you saying that with the headlight switch turned on, neither the brake lights nor tail lights turn on?
Break lights work with the headlight switch turned off?

I didn't know that Honda had a "daytime" running light system. Are you sure, in 1998?

 

Where to start?
First I want to say that from your description, I am gathering that the parking lights in the rear are not working. Is this correct,?? because if the front parking lights are working, that narrows down where I would start looking. The parking lights are separate from the daytime running headlights to my knowledge. Next, you need to have some experience of reading a wiring diagram and at least a 12V test light to run this down. I will give you the diagrams that I have and you can proceed or get some help. The cluster lights are a separate system unless a common connector is the culprit for both. Sometimes this occurs. I would work on the parking lights first though. Here are the diagrams that I have access to. They are small, but copy the pictures and enlarge them with your computer. If you need to find where a particular connector is, ask and I or someone else can provide the answer hopefully. Good luck!