Found an indy Hyundai shop and am in their waiting room now. Their test is free. Should know something soon.

tell me more

Over the counter- most auto parts ,for sure on line.
You dump it in cooling system - like this

https://www.youtube.com/watch?v=CHp5E7XnbXo

Neat test, thanks!

We all know something !
You are welcome !

Shop is stumped. The gauge they put on the radiator cap loses pressure very slowly, but they can't find the leak.

I'd invest in that NAPA kit then as it'll tell you for sure if it's the head gasket leaking.

I'll go with head gasket slow leak into combustion chamber.

There was ZERO evidence of foam in the oil because in my case the leak was going directly into the combustion chamber instead of into an oil passage. No evidence except toward the end when the leakage was so bad I saw steam coming out the tailpipe like when you start a car that sat outside all night in the cold but the steam lasted a lot longer. If you understand air cooled flat six, think bad valve guides the smoke is more than just a puff at start up.

Did they do a careful overall visual inspection for coolant on the outside of the motor and all hoses. Generally, hose leaks drip down and you see it below but, very slow leaks right at the block will evaporate from the heat of the block until it gets really bad. The main concern is that leaks into the combustion chamber will have all kinds of bad effects to rings, hydro lock if there is enough fluid leaking in there...
With mine, we pumped up the pressure to the radiator and there was no water in the oil. We put the regular cap back on and I drove it and then the foam showed up like crazy.

Hoping its a leaking thermostat gasket or water pump. Look for green streaks or do the dye test.

This is sounding very similar to my Ford Winstar head gasket.

It's probably just enough of a leak that the coolant will go into the combustion chamber after shutoff of the engine. Not so bad that the combustion gasses are going into the cooling system such that it's going to boil over. Like that video shows, the kit is testing the gasses in the cooling system for evidence of combustion by-products.
If they did the pressure test on a hot engine (you drove over there, right?) then the testing pushed coolant into the combustion chamber but when the engine is started it's already hot so it is steam/burned to the point it doesn't show out the exhaust.

FWIW, that Taurus we had never showed any signs of a leak on the floor. The white streak down the block on the back side went only halfway down the block. The coolant was evaporating before it dripped. I had never crawled far enough under the car to see it.

had this same thing happen to my 96 chevy. It took about 6-8 yrs slowly lost fluid but no visible leak or drips, no muddy dipstick.

Two yrs ago while passing a car, pow, rod went thru pan, engine gone with only 118000 miles on it.

Instead of trading it in spent almost 6k for new crate motor, new clutch new flywheel and new hoses, runs like a top again.

Did you happen to pull the heads off that motor that blew up?

Ditto. Pressure test shows leak, no visible leak, I'm voting head gasket.

Does your windshield get this sticky film? Do you smell something sweet at times? That would be a leaking heater core. And a wet floor.

That is a neat test and there's a used kit on eBay for $25. I don't even know how to partially drain my radiator. Never touched it before.

The shop tech said it's common for the leak to be due to the porous casting and to add GM "coolant tablets." He said that would seal up the porousness in the casting, if that was the issue. So, after keeping an eye on it for a week or two, he suggested I drop it off at night, so they can check it when it's stone cold in the morning.

I just have a hard time believing the head gasket can be bad. That's not a common issue at all with Hyundai SFs and my mileage is not real high.

Never.

I had a BMW 325e that developed a 'passive' leak similar to your situation. By passive, I mean it leaked coolant into a non-pressurized part of the crankcase. In this case it was a genetic casting flaw in the head that cracked allowing oil into the crankcase. I put some Stop Leak in it and drove it that way for a good six months. I'm not sure the coolant tablets would work but it'd be worth a try IMO. Worst case you'll need to flush the radiator well and put in new coolant when you do get it fixed. The problem with the tablets and Stop Leak is the coolant has to be passing thru the leak in order for them both to work. This is only happening when the engine is stopped after being driven, IMO, and cooling down. You'll have to be methodical in how you put the tablets in, ie put them in a cold radiator, drive the car to warm it up, stop and let it cool completely.
I believe the instructions on the Stop Leak bottle are similar, but it has been a while since this happened to me.

The 96-99 Subaru legacy 4 cam motors with a bad head gasket wouldn't leak water into the cylinders, but the compression gasses would be forced into the cooling system. Tell tale on that one would be bubbling in the overflow tank with the engine running AND the smell of hydrocarbons. Not having all the air purged from the cooling system would also make them bubble. When the gasket was bad and they bubbled, it would force the coolant out of the overflow bottle.

Early Miatas had the dreaded "nipple" failure which was a rubber nipple with a clamp over an unused small water pipe end on the firewall side of the cylinder head.