Glove box pops open under mild acceleration

That's not a glove box cover but a Performance Indicator
Ahhhhh....The memories.
Went for a 'test drive' back in 1971 or so. A 1967 383 4sp GTS that was on a used car lot in Sunnyvale CA. The salesman drove it like it was stolen. Banged off 2nd. glove box banged open. Banged off 3rd....same result. Repeat, same AWESOME results! Didn't buy it ($1200, way too much).
A year later bought my '69 Swinger 340-auto from a Chh...Chev....SHivvy dealer. It chirped 2nd under full throttle....I was sold!