Welcome to the forum!
I don't know a lot of the specifics about that circuit for your model year vehicle, but am wondering whether this is the same situation as before you replaced the cluster dimmer switch, if that is why it was replaced?
Since it's so quick and easy, and if you haven't already, I'd also check to see if the dome lights come on when a different door is opened, in case that part of the problem is just the door switch or frayed wiring to it.
When you wrote that the cluster doesn't adjust, do you mean that it stays on at full brightness, or doesn't come on, and does it turn off if the dimmer switch is rotated all the way to the off position?
If you can dig up a wiring diagram, that might be helpful. There may be a few potential sources linked in my sig below. Without more info, I'd wonder if the replacement dimmer switch is defective, -OR- if the problem is the same with the old switch, then if you have a wiring or connector problem in the circuits to it.
If the switch is very old new stock, and if you can't return it for a refund IF it turns out to be faulty, then I'd try spraying contact cleaner in it and working the switch around, in case it has old, hardened grease in it that is fouling the internal contacts.
