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A way of guessing where the studs are if you are still concerned is to remove one of the outlet covers and find out what side the wall stud is located on the box. If things were somewhat ok you can then measure every 16 inches from there and you should be on each stud.
Still another method is to cut out a one or two inch slot along the entire wall about six inches below the top of the paneling. This will expose the wall joists along the entire wall. Simply take a level and mark the walls where each stud is located. The paneling will cover over the opening you cut.
If you do this, I would then suggest that you forgo the adhesive and just use panel nails to hold it on the wall. This way if you ever decide to remove it you do not end up having to replace the plaster wall, only need to patch it.
Also if the plaster is in poor shape, consider that the paneling will not stick to it very well. As the weakest part of the equation is the plaster being stuck to the lath. And if that is not good, your bead board will come loose and fail.