I am reminded of "Pugsy's Rule". There are no rules. And the first corollary, everyone is different and has different responses. It will be helpful to see what peoples' experiences with specific products are, I think.
Cover-Roll Stretch Tape

First one I tried. Pro: It's tenaciously sticky. Con: It's tenaciously sticky.
This tape is guaranteed to stop mouth leaks for everyone, and I state that as a categorical. This is probably the only product that can be said about. It's so sticky, no amount of drool will loosen it, and, in fact, it's hard to remove. You best remember to fold over a corner of the tape to provide grip to get it off in the morning. This guarantee of efficacy, however, is also it's biggest drawback; those with sensitive skin have reported that repeated use can cause sores and raw skin.
It did not do that for me, however, if I used it regularly for some period of time, I suspect it might. It is so strong, stubble for men won't cause issues, it will stick. I've found you can narrow it by cutting of about 20-25% of its width and it will still be effective as long as you cover the corners of your mouth.