In theory, no, you cannot remove a rejection base socket from an Edison base plug fuse holder, because of the "one-way" anti-tamper spring built into the outside metal shell. That said, I have seen them removed by deliberately destroying the rejection base. There is a tool that will cut off the metal lip at the top of the rejection base, allowing the plastic insert to be pulled out, and then the anti-tamper spring. The last step is to twist out the outside metal shell. It is almost impossible to locate this tool, although a small "Dremel" tool cutter could do the same job (cut off the top metal lip). Another less certain way, is to collapse the rejection base to the center with needle nose pliers, (breaking the plastic insert) and then twist it out. Whatever you do, the entire box MUST be de-energized. If you short out an energized conductor, the 6,000 degree flash (hotter than the surface of the sun) will incinerate anything nearby (like your skin). Before you pick up any tools, put on your safety glasses too.
Replace Fuse Replace socket Replace element
If you are getting power in the socket--replace heating element If you are getting power to the socket, but not through it--replace socket and element
Replace the fuse for the lighter. Also, try removing the penny or dime from the lighter socket and then replace the fuse again.
Replace socket Replace element
Replace: Fuse Socket Element
Check or replace the socket
How to fix the cigar lighter on your Celebrity depends on what is wrong with it. I can't tell from here what is wrong with it, but one of these should do it: It may simply have a blown fuse. If so replace the fuse. The wiring could have failed, again replace the wiring. If the socket is corroded, rusty or has failed altogether then replace the socket. If the lighter itself is failed then replace the lighter.
Dead short in light wires or sockets remove each bulb and socket and replace bulbs one at a time until fuse blows and check wiring to each socket.
After looking below the dash, I found the a primary fuse box with a simple release cover and a fuse diagram identifying all fuses contained there. The fuse for the lighter socket is marked "Cig Lighter" and is on left side. Conveniently located on the right side is a white fuse puller to remove and replace the fuse. The fuse is a blue mini 15 amp fuse.
Locate the fuse box which is under the dash. There is a panel on the end of the dash that can be removed allowing access to the fuses. The fuse you are looking for will either be fuse # 8 Radio/Accessory fuse or fuse # 18. More than likely it is # 18 which is a 15 amp fuse for the front accessory power socket. Pull that fuse and if it is blown replace with the exact same size fuse. If it blows immediately then the socket is defective and will need to be replaced.
dash fuse box Fuse f13
It depends... If the fuse is loose because some foreign object (like a multimeter probe) had been jammed into the socket you might be able to pry the socket closed with a jewlers screwdriver and restore the grip. If that doesn't work, you could insert a thin shim. I have seen this problem when the fuse tap for an after-market foglight kit is removed. The only fix is to put the tap back in because the socket is sprung. If the fuse is loose from overheating...I've seen fuse blocks ruined because the (old style glass) fuse was wrapped with aluminum foil and jammed back in because the fuse kept blowing. If the fuse doesn't burn then something else will. The overheating will take the temper out of the socket and the only fix is to replace the socket. Good luck.