Hello and welcome to Just Answer. My name is ***** ***** I will be happy to assist you with your electrical question.
1) Your voltage measurements indicate a loose wire termination or splice somewhere in the branch circuit.
2) Sounds like you have a shared neutral circuit with a loose neutral connection. Whenever lights dim and get brighter, that is an indicator of a faulty neutral connection.
3) On a properly connected 120 volt circuit, the voltage measurements should be as follows:
A) Hot to Neutral should = approximately 120V
B) Hot to Ground should also = approximately 120V
C) Neutral to Ground should = approximately 0 volts or very close to it
4) In order to correct the problem, the neutral termination or splices need to be checked. Keep in mind that the circuit can tandem thru many boxes as it leaves the main electrical panel. The loose neutral can reside anywhere along it's route either in the main panel or at downstream boxes.
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