Or do a poor man's load test and just attach your voltmeter across the battery terminals, note the voltage as you press and hold the starter button. Even though the battery may show 12.7 volts at rest, that may be a false reading from sitting on the charger all the time. Use the starter to add a load and you will probably see voltage drop like a rock as soon as you hit the starter button. If so, get a new battery. If not, then use your meter to check voltage drop from the positive battery post to the positive stud at the starter, and from the negative battery post to the various chassis grounds. There should be no voltage drop over that short distance. As Twolanerider mentioned, lots of stock Harley battery cables suffered from internal rot, under the insulation where you can't see it. Visual inspections won't tell you as much about cable and connection integrity as a good old voltage drop test.
Jerry