Hi, Dave. The name of the product that you are describing is Peel Away. A few home centers stock it or you can purchase via mail order from places like Woodcraft.
Your description is a little off. Any stripper works by keeping the solvent in contact with the paint. Some, such as the methyl chloride strippers, use a strong solvent that does not have to be in contact long. But these are pretty dangerous to use. The next category uses a safer stripper that has a wax in the solution that forms a thin crust after it is applied. Most people don't know that the crust is there and leaving a stripper on and working for 24 hours is no problem. Citristrip is an example of this kind of stripper. The last category is products like Peel Away. You glop it on like any other stripper and apply the paper to seal the surface. After 24-48 hours, remove the paper and the stripper and paint come away with it.
Personally, I think it is a good idea to have 2 kinds of stripper available, depending on the job. Citristrip is relatively safe to use and works well on clear finishes like on furniture and moldings and low numbers of paint layers. Peel Away is for when you have heavy multiple layers of paint. It is relatively safe to use but less so than Citristrip but it really does the job. I think it is a little more expensive to use than other strippers, but where you need it, you need it. Personally, I will not use methyl chloride based strippers any more. I used them when that was all that was available but the short and long term health effects concern me.
No matter which product or products you choose, please read the label and use all the safety gear, like gloves and eye protection, that the manufacturer suggests. Keep the kids and pets away from the work area.
Good luck and think safety when using these products. Henry in MI