Your readings seem good, a little high but that might be your meter. Batteries typically measure 12.6 to 12.7V unloaded. Your battery at 12.9V seems high, so your meter could be off about 0.2V to 0.3V. That puts your reading in the good zone.
Measuring continuity for grounds does not work well, meters do not measure low Ohms well. That is done as suggested earlier by measuring voltage at grounds with car running and electrical loads on.
The amp gauge may read high if the nuts are loose on the gauge terminals. Make sure you disconnect battery before working on that. There is likely a shunt that is in parallel with meter. Shunts are very low resistance, poor connection there can easily make gauge read high and give voltage drop. Many eliminate the gauge by putting both red and black on one stud. Insulators on studs shrink and disintegrate, resulting in loose connections.
I am no expert on this for a 67, others may chime in with better help. Neither connection is grounded, doing so will short circuit power ... best to check well before hooking battery up.
