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You can do it periodically while it is cooking, but if it is a sweet glaze, wait until the loin is almost finished and apply in the last 20 minutes or so, that way the glaze will not burn.
Not all glazes are created equal so I would hang out on the cautious side and go on the low end for time to start.I've been using some India style sauces as glaze lately and have found that there's a FINE line between awesome and crispy burnt!
I like to get the internal to about 140° -142° and remove the loin (or tenderloin) and put it on a small rack on a tray to catch the glaze. I have my glaze warmed (not hot). Then I figure out which side I want to be up when it gets to the serving platter. Next I paint on my glaze leaving the up side for last, so it will look perfect. Then take the rack back to the pit to set the glaze. 5 minutes or until it looks good. The rack is clean and cold, so the glaze won't stick like it will on a hot grate. And, by not painting on glaze when meat is on the pit, you don't get as much dripping into the coals, where it will burn and smell. If you have everything ready and laid out, you can get your loin back on the pit in a couple of minutes. Here are some racked thighs that went back to the pit on the racks I use, but you get the idea.
Thanks , but the truth of the matter is..... I don't like barbecued food with a glaze and I rarely make it at home. So when I do make sauced or glazed barbecue.... it's either for friends, neighbors, guests, co-workers, or a contest or some small event. Which is the perfect time to show off.... make it look good, and at the same time cook something exactly the way someone likes it because they don't get it very often. The clean-up is always part of cooking over live fire, but sauce creates a mess on your pit, so I learned how to minimize that the hard way.