i put the positive test light clamp on battery positive and the probe in the ground side of the EGG50 connector with the car on and it didn’t light up.
You've probably got this correct, but the EGG50 horn connector should have a red and black wire. Red is 12v from the relay. Black is grounded to the GGG01 ground location. (If you were touching the wrong pin in the connector, that could explain why the test light didn't work.).
If it were me, I would test for continuity from the EGG50 black pin to the GGG01 end of the wire where it grounds. I.e., make sure that part of the wiring harness isn't broken. If you get zero ohms touching those two ends of the wire, then test if you get zero ohms touching EGG50's black pin and any bare metal (including the battery negative post). This would verify that GGG01 is making contact with metal (common ground). There have been assertions that Hyundai's grounding isn't very good. Plus, you mentioned a spare wire hanging loose. Maybe that's GGG01?
Maybe you can accomplish that with the test light. I don't have a test light. Maybe I'm just unfamiliar with how to use one. To me, a multi-meter to test continuity would be clearer.
I also put the test light negative clamp on battery negative and out the probe in the positive side of the connector with my son pushing on the horn and that didn’t light up either.
Did you check the 10amp horn fuse under the dash? That was mentioned in your other thread. I know you're confident that the relay is being energized. But, maybe you're hearing something else?
You can also pull the relay and test it's pinout to see that 12v is reaching the relay when the horn is pushed. This is the relay socket:
You want to check both pin 1 & 5. (#1 energizes the relay's coil. #5 passes through the relay's contact to the horn via #2). 1 & 5 should have 12v when the horn is pressed.
So far, what you're describing is a wiring harness problem. This shows the harness from the relay box to the horn (and to the ground point):
I could understand a broken harness in the sense of the ground not having continuity. Or, the positive wire being broken. The odds of both being broken (which is what you're describing) seems unlikely. That's why I would go further back to the relay and make sure it's really getting 12v, passing 12v.
Checking/fixing the ground from the horn's connector should be easy. That's all right there near the horn location.
You can unwrap the branch of the wiring harness to expose the individual wires. Use a sewing pin to push through the insulation of a specific wire, and test for 12v (and ground continuity) there. That would eliminate whether the EGG50 connector is bad. (Same thing with the GGG01. Unwrap it back a little, test if you have continuity from the EGG50's black pin to the wire terminating at GGG01. If you do, but don't have continuity at the lug, then something's wrong with that GGG01 connector. Like I said above: the next thing would be to ensure GGG01 is making contact with metal -- has continuity to any bare metal or the batter negative post.).
You need to rule things in and out. It's just confusing because you apparently have not just a power or ground problem. You have both. You need to focus on one at a time, and narrow down where the failure is happening.
I took the horn off and home with me and am waiting for test leads to arrive via Amazon tomorrow. I will then test the horn using my car battery tomorrow.
Personally, I wouldn't waste my time testing the horn if you're not getting 12v to the EGG50 connector, nor ground from that connector. It wouldn't hurt to test it. But, the odds of having a broken horn on top of not getting power to the horn (and, on top of not having a ground) seems very unlikely. I think it's very unlikely to have both the no-power and no-ground problems together.
Now that you've got your bumper off, I would seriously consider buying that Fiamm El Grande horn. It's a polyphonic (two-horn) sound. People hear that and they think it's a full-size Chrysler from 1973. There's videos on YouTube showing what it sounds like. I've wanted to do it to my Accent, but haven't been motivated to remove the bumper. If I had to remove the bumper for something else, I'd definitely do it.