You may know this already so pardon me if this sounds too simple - don't buy a little hobby-size bottle of contact cement, buy the little can that looks like a paint can. Use a stiff throwaway paintbrush and paint a thin coat of the cement on the bottom side of the non-skid and also on the rail. Then LET IT SIT for about 10 or 15 minutes to "dry out". This is how it works - when the two surfaces come in contact they will grip like the devil.
It's all on the instructions on the can, but, being a man of the male species you probably won't read them. Who does ?
PS- you cannot re-position the mat once you start to stick it - not at all - here's a little trick I learned from building formica countertops and cabinets: place pieces of 1/8 inch dowel along the bottom piece (the rail) to hold the top piece (the mat) over the place where you wish to position it. When you have it aligned properly slid the dowels out from one end to the other dropping the pieces into contact with each other.