I do not believe you need a new fuse box, I think your have a short or ground issue at where the fuse is. But before we jump to that, let me explain what is most likely going on here. The tail lights are hooked on a system together , where it runs up to where your fuse of course is blowing. Now, even though you say your bulbs are working, what happens is, sense there is a fuse for those bulbs, is the good thing it is operating proper, in the fact of when there is a problem with this circuit ( tail lights to fuse) that it blows the fuse, rather than a fire or melting of wires. Your dash lights are part of same circuit of your talking about running light problem and dash lights. Blinkers and Break lights are on different fuse circuit.
Ok, now that i have explained the mumble jumble mechanical talk, here is what it could be,
When your tail lights are blowing fuses, and it sparks some at fuse box can be only a few things to check out.
Number one, trace wires, especially off fuse box, as well as where they go into the tail lights. This blowing of fuse can be caused by a short in the main power supply into the lights and or a ground that is touch the hot wire. It only takes just a small strand of the hot wire hitting a piece of metal and shorting it out, which would for sure cause fuse to blow and if this hot wire is hitting a piece of metal directly it for sure will cause the fuse to spark big time, when trying to put in a new fuse. The other issue is where the fuse goes into the slot, could be bad connection, or corrosion if got wet.
I personally believe your problem is not your fuse box unless it got wet or really looks bad. I believe your problem is going to be a ground wire from the taillights, (most likely at the lights them self at rear of car) thats rubbing up the hot lead on the wire or the little prong connectors. Your tail lights have a connector on them that plug into the tail lights, check those to see if there clean and look good, if there not replace them. Auto Zone can help you to get right ones to put on to connect. Only other thing is at the rear most likely where your tail lights are is the hot lead is hitting a ground wire of piece of metal, which of course will short it out. Conclusion: I think the problem you will find is at your tail light connections of where it goes into the tail lights. This would cause exact symptoms you describe, Fuse box, i doubt as you would have lots of other issues with other controls. Thanks Mike from Fixya,