There is something to be said for installing a tube but also to me more to be said against doing so. If the tire is not in really bad shape I much rather work with a tubeless as a nail on such in it does not deflate as fast as most likely with with a tube. You normally can fix a tubeless while still on the machine and not have to break the tire down. Of course you have to be sure the reason for the leak in the tubeless is taken care of before installing the tube. Meaning remove any nail or such.
Having said that I have had tires and rims tube was only solution.
I can vouch for the soapy water spray to show up with bubbles. Forty some years ago when working on sealed refrigeration systems that is what we used. Also be sure you check around the tire and rim to verify it is not leaking there. I have gotten trash pressed in there and not notice it.
Hey, be sure you are running as high a pressure as you are suppose to. Low air pressure can allow tire to rim contact to loosen as you place side loads on the tire. Maybe working a slope or making a turn.