I have a mid-'70s Univox Coily guitar. I love it, but the neck pickup has gone dead in a weird way.

Let me explain:

When selected, the neck pickup does put out some sound, but only microphonically. I can yell through the pickup, but the guitar sound that comes through is very quiet and comes with a significant hum. The hum is also present when the middle position is selected, but not in the bridge position.

I don't have a multimeter, and I'll admit that my electronics expertise leaves quite a bit to be desired. That said, logic tells me that if there is a signal coming from the pickup at all, even if it is only microphonic, that the windings are somewhat intact - intact enough for my voice to vibrate some of the coils and send that microphonic signal to the output of the guitar. But it seems that the break in the winding is situated such that the signal generated by the guitar strings' vibrations passing through the polepieces' magnetic fields is not able to get through.

Does that sound right? If it is, the only option is to attempt to rewind the pickup, yes?
I can't imagine that the magnet in that pickup has gone completely dead, although I don't know what kind of magnets are in these pickups.

If it helps, the Univox Coily is a fully-hollow guitar with two single-coil pickups that look like staple-top Hofner humbuckers with plastic covers spray-painted silver. There is a row of screws and a row of small metal rectangles that come through the covers. The guitar dates from the mid-70s, and was made, I believe, at the Matsumoku factory in Japan.

Any ideas about how to deal with this problem, myself, on the cheap (b/c I have no other choice) would be most appreciated.
And any ideas about putting together a simple pickup-rewinding jig, or about what wire to use, would be most appreciated. I just don't want to replace the pickup, since you can't buy these, really, and I really like the sound of them. Just want to get it back to working condition...
I know that I need to pick up a multimeter, but I'm BROKE right now, and can't do so yet. In a coupla weeks, maybe. But I guess I mostly want to know if my guess sounds plausible, and if there are other conditions that could cause what's happening. Anybody?
Could be dozens of problems, a bad connection in a number of places, maybe its shorting somewhere, maybe its a grounding issue. IDK, ive never had the kind of problem you are having. Without a multimeter, it will be very difficult for you to narrow down the problem.
You can get one for 10-$20 on amazon.
Another choice would be to look for a replacement on ebay.
I'll try to borrow one, or pick one up on the cheap. But I don't know what to look for. What readings would indicate what problems, and so forth. Is there a good resource anyone could recommend?
DC resistance will allow you to test for continuity. Resistance is measured in ohms. So if your coil is good, you should expect 2k-7k (or there abouts, depends on the pickup) ohms resistance. The k means thousand. If you have a broken coil, that number will be inifinite or just ubsurdly high, if you have a short, it will be to low. If you have a normal reading then your problem is most likely elsewhere. My thought is that it could be a bad solder joint or switch or something along those lines. Sometimes the wiring in the guitar can have a microphonic effect as well. You might be able to find a meter as cheap as $5 from a super cheapo tool store such as harbor freight.
Pickups are very hardy devices. There are no moving parts. A coil around a magnet. There isn't much that can go wrong.

Unless you're the kind of person who keeps doing a/b comparisons by switching pickups out every other day

Like other have said, it could be a bad joint, a bad ground or a selector switch problem.

I usually suspect the actual pickup last
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