The socket & lead set shown in the photo should be replaced. The socket and the two insulated leads are permanently assembled in manufacture.
If you have the Durst M601 dichroic color head, it takes the 12-volt 100-Watt 2-pin GZ6.35 base, MR-16 reflector EFP lamp.
Thus, you need a GZ6.35 2-pin ceramic base socket & lead set. ........
Shop for a reasonable price before ordering. It might be useful to search the Internet for suppliers in your area. Use the search string “GZ6.35 socket” in Google or whatever search engine you prefer. If you have more than one of these machines to maintain, it is a good idea to purchase several replacement sockets for future use when needed.