I'm not saying this IS your problem, but while personally diagnosing blown head gaskets, I've used a several methods. I don't work on cars for a living, but I do dive in deeper than most guys would dare to. One thing I really must know, for sure, is does it really have a blown head gasket or not. A stuck EGR valve will put oil out the tailpipe. You want to make sure what is coming out the pipe, first.
'Cylinder leakdown' method, 'dye checking for combustion gasses in the coolant' method, 'litmus paper test strips', and the 'air bubbles out the radiator cap' tests are all methods I've used over the years.
A "cylinder leakdown test" which requires some tools (cylinder leakdown gauge and regulator tool, an air compressor capable of a constant 80-100psi, etc) along with removing each sparkplug, some knowlege of valve timing, and often a way to keep air pressure from pushing the piston down the bore from the 100psi of air pressure. It's the most direct reading and scientific of the methods, but takes the longest and isn't 100%. The idea is that by pressurizing the combustion chamber, measuring the leakage differential (using a dual gauge leakdown checker) will tell you percentage of leak, and give you a good idea of where the air is escaping. I own a Tavia brand dual gauge type that I bought through Jegs.
(
JEGS Performance Products 80520: Dual Gauge Leak-Down Tester | JEGS)
You can also use the hose that comes with some compression testers, but you really want to regulate and measure psi someway. You pressurize the combustion chamber at the sparkplug hole, open the radiator cap or degas bottle cap and look for bubbles, or listen for escaping air if the system is drained. Sometimes 100psi isn't enough pressure to simulate 300psi-1200psi experienced in a running engine, and you can get a false negative. This happened to me once. Still, if the combustion chamber has even a moderate sized path to the cooling circuit, opening the degas bottle cap and pressurizing each cylinder one at a time through it's sparkplug hole is a pretty good test. It won't however, tell you if you have a coolant to oil system leak. But there's the 'milkshake test' for that :-)
Dye checking for combustion gasses with a kit from Napa (
https://www.napaonline.com/en/p/BK_7001006) has worked well for me. You drain and flush the system a couple times, run the engine long enough to open the thermostat (or better, remove the thermostat before stating the test). You sample the cooling water and add a few drops of dye that comes with the kit. Then just read the color against the chart. You can get cross contamination form your hands, fumes in the shop, so it's best to repeat the test a couple times to limit the chances of getting a false positive.
The paper strips are junk, they go bad after a few months if not kept in an airtight container. My local auto parts store had some that came in a non-airtight container, and didn't work, showed a false negative if I remember right. (
https://www.amazon.com/Cool-Trak-311...asket+test+kit)
The air bubbles test has worked the best for me. You purchase a Lisle radiator funnel with the degas bottle and adapters (Lisle-24680). Attached, you run the engine, using the funnel to re-fill the cooling system more than full (such that the funnel is always at the halfway mark) You purge the cooling system of air, kneading the radiator hoses expelling trapped air, lettin gthe engine come up to full temperature. You keep the funnel attached, and full to the halfway mark at all times. Once you're sure all the trapped air is out, you look into the funnel like it's a wishing well, watching for air bubbles, sometimes for 20 minutes. Holding the rpms at 1500-1800 helps. If you have a 'blown head gasket', a leak between the cooling system and the combustion chamber, it won't stop blowing tiny bubbles. At idle (under high vacuum), the coolant level will often continue going down, where the intake cycle draws cooling water into the cylinder, and pumps it out the tailpipe.
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