Lighting, Light Fixtures, Ceiling and Exhaust Fans - 6-way (3 arm) Torchiere needs switch and wire

I am trying to rewire a 1930's model Torchiere with 3-arms on a pull chain and a mogul at the top. I have purchased a pull chain 2 circuit switch for the operation of the arm lamps. It has 3 wires: black marked L, red marked 1 and then blue marked 2. Each arm on lamp has both black and white wires intact and in great condition. I will be replacing the mogul with a standard socket for a cfl. I am confused as to how the 2 circuit switch gets wired to the arms. All of the existing black arm wires are twisted together and the black wire on the existing broken switch is hanging free. The main wire for the lamp is of course gone so I cannot copy the original work. The white wires from the arms are connected to the old switch, one on a brown wire and 2 on a red wire. Please help

The first thing you need to do is to identify which color wires on the lamp attach to the center post of the bulb socket (hot) and which color attaches to the screw shell of the socket (neutral).

The switch should be inline with the center post hot wires.

The black wire on the switch is the "input" which will connect to the incoming hot wire from the cord. The red and blue are "outputs" which will connect to the hots going to each arm of the lamp.

The two neutrals from the lamp arms will connect to the neutral from the cord which is usually identified by a white line or ribbed texture on one side of the lamp cord.

If I understand what you are saying, I will not be wiring this lamp in any way like it was wired 80 years ago. I don't really care as long as it works. So, does it sound like my lamp had its white and black arm wires switched to you? That is the only thing that is making sense to me right now. If that is what is wrong then no wonder I was so confused. So, can I attach the black wire from the switch and a power line to my socket (which will have its own switch) to the incoming hot wire and then take the white wires off the old switch and attach them along with a nuetral from my socket to the nuetral incoming and then untwist those black wires and attach them to my switch 2 on red and 1 on blue? I just want to be sure that my translation of your post is accurate. Thank you so much for your time.