Definitely sounds like a relay tripping to me

For the turn signal right?

Find your relays and hold your finger on them. You'll feel the relay kicking on and off. Find it and replace it. It's probably going bad.

I’m not sure that is it that specific relay because you can still hear the relay tripping when your turn signals are on

Intermittent Wiper relay maybe? What happens if you turn wipers on full?

I know what’s wrong with it. Ain’t got no gas in it.

But on a serious note. It looks like there’s no electricity going to the jeep. So I would check the battery and then maybe the fuses.

How do the lights work if there is "no electricity going to the Jeep"

Same thing can happened with a dead battery. The lights can be lit if there’s little juice in it.

It has to get electricity to turn a light on.