Dan,
Looks likle Paul has set you straight regading the wiring to the regulator. But there are a couple other things you may need to understand as you go forward.
If the regulator is an original type, and not a solid-state replacement type , the output will NOT read 10 V on any multimeter. Intead it is Battery voltage (nominal 12.6 V) but going on/off about 2 times per second. The average voltage of the on/off is 10 V, but because of the On/off 2 times per second it is virtually impossible to read the average. On a digital multimeter you will just see what looks like random numbers jumping around. If you measure a steady 12 V, the regulator is stuck ON. If you read 0 V, the regulator is stuck OFF,or something is not connected. Be sure the regulator case is grounded. If you measure a steady 10 V, then you have a solid-state replacement regulator. If you don't have a multimeter, you can test these voltages with a 12 V test lamp. If the regulator is working correctly you will clearly see the test lamp blinking On/OFF. And if it stuck ON, you can see that the light is same brightness, whether you test the B terminal or the "I" terminal. If it's a solid state reguulator you will see a steady, slightly lower brightness when testing the"I" terminal.
Regarding the connections to the gauges, mattinoz is incorrect. It will not matter which terminal you connect to on the gauge. Most common gauges ARE polarity dependent, but the SIII thru SV gauges are not. They operate by means a small heater inside that heats a bi-metal strip that moves the needle in proportion to the current thru the heating element. And heating element is not polarity dependent. It's because it uses this "slow reacting" heater element that the needle reads pretty steady even as the regulator puts out an ON / OFF 12 v.
Hope this helps,
Tom