Hello. Welcome to Just Answer.

How many locations are affected by the partial outage? Outside light, switch for outside light, overhead light, switch for overhead light (are we talking about one overhead light, or two... stove exhaust fan/light). Is it 5 locations, or 3, total?

Are you comfortable opening boxes at those 4 locations, to look for a loose connection? I would start with the two locations that were initially involved (outside light, switch for outside light). This will most likely be a loose splice, probably on a set of white wires... but it could also be on the black wires.

OK, then I would move on to one of the other boxes that isn't currently working. I doubt the problem is in the exhaust hood, so I would check there last. Also, the wire could be loose at a WORKING light, light switch, or outlet box. Would you like me to explain how that's possible, or do you already know?

What type of tester are you using? Do you know which breaker feeds that circuit?

Are you getting that reading at the breaker?

I would turn all lights in that area on, and then turn the breaker off. Make note of which lights go out when the breaker is turned off. All of those lights are potential locations for the loose connection. If possible, try to determine which outlets lose power as well when that breaker is turned off. Those are also potential locations for the loose connection.