A neon glow-discharge plasma supports multimode oscillation in the form of traveling normal modes of p-type neon-ionization waves. The modes compete as coupled spatiotemporal oscillators, each capable of driving the other or being driven. Competition is modulated by neon-resonant laser light chopped almost synchronously with the subdominant wave mode resulting in quasiperiodic mode hopping between neighbor wave modes. This process repeats indefinitely without adjustment of the discharge plasma or chopped laser-light parameters. The mode-amplitude normalization of the driving-force term in the governing differential equations, inherent in driven-oscillator phenomena and responsible for quasiperiodic mode hopping, is validated by experimental observations.