Well I would first go back to the new radio.
From your description the dash lights worked fine until you removed the covers to get the old radio out.
Did you disconnect any ground wires?
The old radio illumination wire is an "end user" of power from light switch and dimmer, so not being connected wouldn't effect dash lights.
Did the new radio fit OK?
Maybe pushing it into place caused connector behind it to be pushed and disconnect.
I wouldn't start cutting any wires or searching other areas of the dashboard, I would pull out new radio and check connections there.
Test if dash lights work with new radio out and any new wiring harness disconnected.
Yes, light blue/red stripe wire is used for ALL the lights hooked to dimmer module, same wire color has been used since at least 1990
Ranger Radio wiring diagrams here: Ford Ranger Radio Wiring Diagram
2004 had 3 radio options, so 3 wiring diagrams