Theres a lot of work in Zeniths as there notorious for that issue. If you see some that are cracked but bare wire isn't showing so they wont have the potential of shorting I would leave them alone, but the wire that has the rubber insulation that has fallen off I would tackle first. Wiring in the RF and IF sections can be critical as to the original layout. I would suggest taking a high resolution Camera and photographing different perspective of the wire placement and components.
Most wiring for extension cords usually has a tag on it telling the current rating and the size of the wire. Usually 18 and 20 gauge so that would give you a perspective to size. Multi-strand wire is OK but you have to make sure that the wires are not nicked or missing to be safe. Don't use automotive wire in the high voltage sections as the insulation breakdown voltage should meet the volt required.
The rule is the smaller the gauge number, the larger the wire. (Goofy as it may be)
house wiring is usually solid but for appliances such as lamps fans etc are multi-stranded for flexibility.
here is a chart on wire size.
I would suggest 20 or 22 gauge
You can also get a wire gauge from Hobby stores, hardware stores LOWES, Ace Hardware or electric supply and building materials store, online EBay or Amazon and Tool shops like Starret tools (They are EXPENSIVE) but Harbor Freight has them much Cheaper.
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