Were you measuring the positive (+) voltage at the connector with the multimeter grounded on the body/chassis or grounded through the pin(s) at the connector? The multimeter's black probe needs to be grounded on the body/chassis/battery to get a true reading. Try again and post the actual voltage(s) that you are seeing at the connector pin.
You also need to take a continuity reading in Ohms between the negative (-) pin(s) at the connector and the battery's negative (-) terminal to check for excessive resistance. Normal resistance should be close to zero Ohms. Please post all of you readings here after retesting.
As others stated, be careful how you use the multimeter to prevent shorting a circuit to ground. This is a situation where using a Power Probe tester would be the proper way to protect the sensitive electronics. As a minimum, I suggest taking advantage of the Harbor Freight 15% off coupon to buy this rudimentary safe-probe.
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