Your probably not having an "oil" problem. The ignition system sends electrical current to the spark plugs to fire and keep the engine burning fuel. If the ignition system stops sending electrical current the engine stops running, oil pressure drops, causing the "oil" light to come on. Another way to look at it is, if you use the kill switch on the handle bars you get the same issue. Engine stops running and the oil light comes on...NORMAL.

Often a problem comes from the last thing someone messed with. Since you changed your battery, I would suggest making sure the battery connections are good and tight. I'm new to the Goldwing but motorcycles can have funny intermittent problems with even slightly loose battery connections. Make sure to put a wrench on the connection bolt. Don't try to break them just good and snug.