Help me figure out how to remove the furnace on my Pop Up

The "switch" you are talking about is the sail switch. They sometimes stick. Can you lube it without removing the furnace? If you can get it to move it, you should be able to get some lube on it and save yourself a lot of work???

From your picture, I'm not sure what you are having trouble with in trying to remove the entire unit. I'm trying to help, but as usual, I'm a little confused.