Actually, you shouldn't need to get it out...if it's the original setup, you can get to it from the glovebox side, should give you enough room to pull and clean the contacts, reconnect and test it all whilst in place.
Probably should have said that you can test it all before you put all the panels back in place.
Also, the mention of things looking a bit green suggests that the contact cleaner might come in handy.
Wishing you success.