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We report evidence for the first generation of XUV spectra from relativistic surface high-harmonic generation (SHHG) on plasma mirrors at a kilohertz repetition rate, emitted simultaneously with energetic electrons. SHHG spectra and electron angular distributions are measured as a function of the experimentally controlled plasma density gradient scale length Lg for three increasingly short and intense driving pulses: 24 fs and a0=1.1, 8 fs and a0=1.6, and finally 4 fs and a0≈2.1, where a0 is the peak vector potential normalized by mec/e with the elementary charge e, the electron rest mass me, and the vacuum light velocity c. For all driver pulses, we observe correlated relativistic SHHG and electron emission in the range Lg∈λ/20,λ/4, with an optimum gradient scale length of Lg≈λ/10. This universal optimal Lg-range is rationalized by deriving a direct intensity-independent link between the scale length Lg and an effective similarity parameter for relativistic laser-plasma interactions.