Our 1979 was mounted to the wall on the sides, bottom and top. The bottom actually went behind and underneath the countertop; the top under the overhead bin IIRC. They were rivet to the wall at those points so the tambor and track were inside the rivet lines.
Ours broke up on removal since the 30 year old plastic had weakened over the years.
Tadd, Beth, Grundgetta and Weeble
Proud to be Air #37137