If Tail lights and Brake lights work normally before trying Hazards, I would suspect the hazard relay or the column switch. You can move your turn signal relay to the hazard spot on the fuse block easily enough to rule that out first. I hope its not the column switch (I just swapped mine out because my hazard connector was broke off) and its not that simple to do.

I like the idea your tail light fuse is just to low a value as well.