I like to smack the tire against the ground a few times with the puncture side down
Of the two times I had a tubeless road puncture, the one time it didn’t seal was on a ride out in mild sunny weather. The one time it sealed up was while I was riding in the rain. Go figure.
Dynaplugs worked great on my offroad tubeless punctures, but these road gashes seemed too small to put a plug through.
It happens, but if the bead seats and the tire holds air 
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I’ve found that so long as the tape job is good the main place I have sealant getting under the tape is via the valve hole due to the rubber seal round the valve stem base not being fully sealed.
I have have HED Emporia’s that have a DEEP center groove that’s almost impossible to get the tape to stick in AND on to the shoulders. I’ve taken to using a heat shrink gun to get the tape flexible enough for it to get all the way into the channel and shoulders. They are also super sensitive to a good seal around the valve stem as well.
A hack I learned from someone on YouTube is to put a layer of electrical tape over re-installed tubeless rim tape. This is most relevant if you’ve had to replace the rim tape, as us mere mortals can’t do as good of a job as the factory.
I was struggling with a good seal with my rim tape application. The electrical tape got me that last needed bit.
“Jason” taped my front wheel, it looked like a factory tape job. Perfect then, perfect now. I guess he is an immortal? LOL. Same bike shop, another guy taped my rear wheel and it didn’t seal perfectly and some sealant got underneath and all the way to the valve stem. They re-tapped it for free and same thing. At first it was losing some air overnight, but now not so much. @webdev511 I guess the next tape job I’ll insist that Jason do it.
Got my gravel bike in May 2021 and have only ridden road since then. On tubeless 30mm and I can’t imagine why anyone wouldn’t want to go tubeless. Never had a flat really until my sealant was running real low and I got a tear, but this was quickly sealed up. Probably wouldn’t have happened if I re-filled the sealant on time. But that was the only flat I’ve had and I don’t ride on smooth tarmac all time, plenty of back roads with debris and what not. Now I know better when to refill sealant.
A bike fitter told me I absolutely have to replace the tire due to the tear, but I never did and have had no problems in the 1.5 years since.
I’ve had to resort to gorilla tape more than once. Oddly enough it only takes one wrap then it’s golden, just NEVER take it off…because it won’t come off cleanly. Don’t ask me how I know.
Ditto 
ALWAYS put a patch on the inside.
Putting a dab of sealant on the spot before screwing the valve down can help those little leaks sometimes.
Thing is, I’ve gone that long with zero punctures on clinchers before, similar riding. And do so to this day. Modern tyres, especially GP5000 are way better for avoiding flats regardless of tubeless, to the point that it feels like madness.
I presently have one tubeless road bike, 1 tubeless gravel, 1 tubed road bike, and have had more flats on the tubeless road bike. Largely due to a poor set of Hutchinson Fusion tyres perhaps, but still - the sealant was not enough.
I think you need run the crucible of unsealable puncture, face full of sealant, run out of plugs, remove tyre & valve to install a tube, cycle another 50 miles covered in goo before you can really judge.
The sealant under the tape is fine IMO, its sealing the gap!
I wouldn’t cut the tape diagonal at the end though, you just create a longer edge and possible gap.
For taping a wheel, I’ve found it best to put a bit of stretch in the tape, it slots in easier and sits nicer. Not had to resort to sticking extra tape on top yet!
and do it with the wheel on the bike in a stand. that way you can get a good amount of tension on the tape and keep it even inside the rim. Quality of tape matters too. The thicker opaque tape from WTB/Stans is my choice for base layer, then I use some stuff I have experience with from my years in wafer fab equipment if I need to build up another layer or two to get the bead to seat.
Getting the tape to adhere smoothly isn’t that hard, you just have to be slow and methodical about it. I like to extend the tape a couple of inches at a time, keep it under good tension, and press it down firmly with my thumb to eliminate any air bubbles.
I didn’t tape it, next time in the shop I’ll ask ‘why did you cut a diagonal, seems like it creates a longer edge for sealant to get under’ in my best ‘just a curious engineer’ voice. And call ahead and ask if Jason will be in the shop, because that guy makes tape look like a factory machine installed it.
Tell them not to use muc off tape as well, worst stuff I’ve ever had the misfortune to use (helping someone at their place and they’d bought it).
muc off tape has been great in my experience… extremely tenacious/gummy adhesive which I consider a good thing. I get good results too with a variety of other tapes depending on what I have on hand.
proper stretch/tension, proper width of tape vs. rim bed width, use of a heat gun to set the tape, keeping things clean and oil free, setting overnight with tube if possible, not cutting end under tension, and using a towel or something conformable to really press the tape into the rim bed are all little tricks and things to watch out for.
shop mechanics love it when their customers start with “as an engineer…” 
I heard about this sealant on a nerd alert podcast with mtb race mechanic Brad Copeland.
I ordered some from Europe a few months ago, and then also ordered some MaxaLami Wurstwasser which AFAIK is the exact same sealant.
So far I am using it in my road/gravel/mtb setups and am finding it to work really really well.
The formulation seems distinct from the typical latex/ammonia type sealants.
I think tubeless tire tech has gotten a lot better with the more recent tubeless tires from various brands.
Latex sealant is still a crappy experience though, with little innovation from the companies selling it.
I can appreciate Stan’s being pretty much the first with tubeless sealant, but don’t feel like giving orange seal any more of my money.