Lights Dim Shortly After Being Turned On?

I recently purchased a home and it looks like the basement was finished by the owner after it was built. In the basement only, not upstairs, the lights and lamps start at regular brightness when turned on, then dim down to about 1/2 about a minute later, without other loads being turned on.

Something must be wired wrong somewhere. There are a couple dozen outlets, 2 overhead lights, over a dozen cans, and a ceiling fan/light with remote control. Possibly related, a GFCI upstairs trips daily, after being replaced twice, with just 2 small items on the circuit.

By Bob W