1997 Eddie Bauer power antenna

If the motor still runs usually it is just a broken "cable-type thingy" inside the antenna mast which is relatively easy to replace from topside (rather than taking the whole thing off which requires access through the wheel well).

Try a google group

search for "ford explorer power antenna replacement" and you will find lots on this.

I've changed a few of these things and have always had to remove the power unit, disassemble to get the old broken piece of the geared cable out. Is there some other way?

On mine, you can run the geared plastic thing in and out (to inspect or change it) if you remove the top cowling and the locknut and have a helper operate the antenna motor. If the problem is the motor or the running gears inside then you need to take the whole thing off from below.