Hi Rog, I just looked up a John Wanamaker clock and as you say it has a dome its most likely a 400 day clock so its safe to say the plates are lacquered, if you use a strong enough cleaner it can turn the lacquer into a slimy goo. The old British Smiths clocks are known for this. If the plates looked fairly clean before you cleaned them then this was probably the case, compared to untreated brass it almost looks like gold when lacquered. I dont know anything about how to re lacqure plates, I imagine its a pain in the butt as you would have to clean out all traces from the pivot and screw holes afterwards. If it was me I would just clean off any leftover traces and then put it back together. Its only there in the first place to keep the plates looking nice as you will know by now how brass looks when it gets tarnished. I am sure someone else will be along soon to let us know if there is a way to re-lacquer and what to use. The laquer is not essential it just means it will eventualy tarnish. You will probably find things like the barrel case etc were also lacquered. If you are new to clock repair one thing I would add is that these clocks can be a real pain to set up again once you have it back together. Try and get yourself a good book that tells you how to do it, it can at times be a long process and if you should break the suspension spring this can also be a big headache, probably not the best type of clock to start with.
Please dont let me put you off, keep at it and you will get there, if you get stuck we will do what we can to help you through 
