I took this project on last year. I don't recall what brand of string I used (Gator?) but was able to find it 0.130 diameter. I ended up replacing the complete length of the string which required dismantling the entire antenna mast. Yes, the tip screws off. Some people actually glued them back in the day to keep the tip from being stolen, use heat sparingly though. Each section has a brass insert crimped to keep the mast from disassembling itself when retracted. I used a dremel cut-off wheel and cut just above each crimp (keep the brass insert for later use).
When fully disassembled you will have a small pin that holds the line in the final antenna section. Remove the pin, if the line does not pull out then just drill out (be sure to be centered). Once you have it out measure what length cut it. The end of your line you plan to insert use 80 grit paper and scuff. I used gorilla glue (thin coat), insert into the antenna section and let cure, once cured then drill hole for pin and force pin through. You're ready for reassembly. As you reassemble each antenna section insert the brass insert and crimp. You antenna is ready for reassembly.
My housing was corroded so I stuck it in the blasting cabinet, cleaned it up, lubed what needed (gears) lubed and reassembled. Looks and works like new.