A couple of comments on this:
The first is that you can find even a pretty slow leak with a spray bottle of soapy water or something like Windex (or the cheaper generic thereof), albeit, I don’t know the logistics of carrying even a small one on a motorcycle. But anyway, you spray around the plug and wait for bubbles.
Second, if you were to spray around an embedded nail like the one in the picture, and not get bubbles, because it was in that tightly, I still wouldn’t drive on it, because it’s rigid, and the movement of the tire could dislodge it enough to start a slow, or even fast leak. That won’t happen with a flexible plug.
Third, I have run on plugged tires for more than a year. Probably could more than that, but if a tire still under warranty picks up a nail, I take it in for replacement. A tire out of warranty rarely has more than a year left on it, and frankly, in my opinion, isn’t worth taking in to have patched, because if you are paying for dismount and mount, plus balance, you might as well get a new tire. You are just going to be paying that again in a year for the new one you need anyway.
Fourth, for people taking this advice for cars, keep an inflator in your car that hooks up to the 12V power outlet (formerly known as “cigarette lighter”). These cost about $25, maybe (I paid $15 for mine at Walmart about 20 years ago, but now they have a few extras, like being able to set the stop point). I have limped many a slow leak to my next paycheck with them. If it’s a leak that needs to be filled something like once a week, they are great.
They are also great for when you pick up a nail on your way to work, and come out at the end of the day to a flat tire. If you also have the plug kit and spray bottle, you have a few choices, besides changing the tire.
You can pump it up, and spray around the nail to see how fast it is leaking, while Googling the nearest tire place, and calculate your chances of getting there before it is flat again.
You can pump it up, plug it, and possibly forget about it.
You can pump it up, plug it, and when you have time, drive it to a tire place.
I don’t personally hate changing tires, though, if it isn’t raining, and it’s a good thing to know how to do, because a tire that genuinely cannot be fixed doesn’t put you off the road: you take it off & put on the spare; the next morning, you leave a little early, drop just the tire and wheel of at a mechanics’, drive to work, and pick it up after work. If you call to say you are coming, they will probably be ready to put the tire right on for you using a floor jack, so you don’t have to wait for an open bay.
Just remember-- every time you air up your tires-- that you have 5, not 4.