Ditto on Broncobill78's comment, check all you r cables and connections in the battery circuit. An easy way to see if you have a bad ground to scrape a clean spot on the engine block and check between that and the battery negative post. If you are getting a voltage reading, the ground is bad. could be the connections to the cable itself. You need a good ground to allow the battery to charge. Also the starter solinoid is mounted on the fender. The pick coil for the solinoid is grounded to the fender so if you don't have a good ground to the fender, it will either not operate or will be flaky, and that goes for the alternator also, it will work poorly or not at all if the ground from the alternator case to the battery negative is bad. Bad grounds are probably the major cause of flaky problems. Also check the condition of the positive cables, alternator to battery, battery to solinoid and solinoid to starter. Speaking of starter, sit grounds through it's case also, so that is another place to check. It wouldn't hurt to go through all ground connections by removing, cleaning the connection and checking the wire and connector. That may seem like a lot of work, but in the long run you will have less problems. I'd do the same for the (+) connection from battery to starter.
As for fusible links, the only one that would prevent battery charging is the one on the end of the cable from the alternator to the battery, (usually attached to the battery side of the starter solinoid).
Good luck,
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