On the NG you have to cycle the reversers 5 times (full open/close cycle) to clear the engine accessory unit fault history and hence get rid of the reverser light.
I remember when I had just checked out as a newbie F/O on the NG and we had the reverser light on after push-back (I think it was when doing MC recall check). The end result was we returned to the bay and had the MEL apllied which involved having said reverser locked out.
Just curious, but are you guys suggesting that this was not necessary and we should have just cycled the reversers 5 times and all would have been fixed and we would be on our way with both reversers working normally?