Ask the guys at Monarch, they would know. I'll bet they would say "sometimes". You can clip the fabric insulation off and have it tested, should be less than $20. I would just write Monarch.
Monarch had already been asked. See first post.
Can they tell from records? No. Not directly.
The best they might be able to do would be to identify the suppliers from whom Monarch Machine Tool purchased bulk wire
OR pre-built wiring "harnesses" - much as the automakers do. If a pre-built harness, then THAT supplier's records would have had to have survived to ascertain from whom their bulk machine tool wire had been purchased.
Next step would be to hope the maker of the bulk wire had records for that period of time.
That's rather expensive detective work if you have to pay to have it done, yah?
Most especially in the face of a typical 7-year records retention policy for mundane administrative details of purchasing and the like. It isn't the same as a casting pattern or a blueprint.
My bet is that for all the records Monarch still have, this is not the sort of information that would have been preserved. It had no value. If they need to rewire a rebuild, they use present-day high grade wire, not spools of wire rat-holed in 1939.
If indeed, it can be cheaply tested? Go for that if you think it matters.
The risks were the result of poor handling practice on a grand scale. The dangers are - and were - otherwise overhyped. Liberty ships? A Uncle went onto those right out of HS, spent the next 50 years in their Engineering spaces. His demise at a good old age was unrelated to asbestos. Heart just finally wore-out. Building them or cutting them up for scrap them was where the risk was. Same again with buildings and asbestos insulation and fireproofing.
I've worked a lot of asbestos, still use it now and then. My grandparents home was shingled with it, late 1940's, still is. Durable stuff, asbestos cement shingles.
Most of the family lived into their mid to late 90's.
Millions of residences had "asbestos plastic" flooring tile. I'm sitting IN one of those, now nearly all porcelain tile instead. If you must worry, that tile will be easier to find. I can even give you some to play with, if that's flavour-of-the-month for OCD'ing!
Meanwhile .. 10EE.. The wire in my 10EE's (1942, 1944) does not look like or feel like ANY of the asbestos-reinforced insulating jackets I've ever seen.
Nor does the Cambric sleeving. It is ignorant linen, as was bog-standard in that era, just dirtier for the passage of time than average. I might have a few inches of the original around. ISTR the new stuff is Dacron polyester?
Hmmmmm...... is polyester safe?