> AM radio/coffee maker timer
i.e., a Clock-Radio, perhaps with an extra external timered outlet.
That complicates the re-wiring slightly.
The clock has to get power ALL the time. (I know you don't need another clock, but you can't have a clock that's wrong most of the day.)
The clock is fairly safe. (Little finger-exposure, teeny fire risk.)
OTOH, the isolation transformer *probably* should not be live 24/7. It's probably OK, but it does vampire a little power, it won't live forever, it may stink when it fails, and leaving it on hastens that day.
So we have to work-out how the clock and radio are inter-wired, so we know where to put the isolation. Also how the new ground wire goes.
Wires may be P-2-P or all Y-ed together. They may all be black or they may be black/white or who-knows. The trigger and switch will be hidden on the clock motor, but the wires will run about like this.
You also have a percolator timer? (No Mr Coffee drip when this radio was made!) This may be the same or a separate switch. There may be a switch to chose radio, coffee, or both (or neither). If you are not needing a coffee timer, you can probably ignore the outlet and leave any switching on Radio.
IAC, a Lamp Limiter will be very wise.