Anyone that works on old tube radios can likely fix the reverb unit. I had an old mid 60s console stereo once that had one. Kind of neat at first, but gets old fast. You may not want to invest the money. IIRC the main component is a "vibrator" tube, which may be hard to find/expensive.
Not cheap, but you need only one, ever: solid-state (them new-fangled transistor thingies) vibrator replacement.
You'll thank for for eliminating all the sexy vibrators from the google search.