I have light on "brights", but not dims on passenger side of 2004 jeep grand cherokee

I have a 94 JCG also and my right headlight burned out also. The only way to change this out is to take out the battery entirely from the vehicle to get behind the headlight to put in a new bulb. Not that hard to do but just annoying that you have to remove the battery from the car. Get the replacement bulb from an auto store and you'll see it's not that big a deal to do. Maybe you can ask the auto store employee to help you do it.