  We present a blind search for doublet intergalactic metal absorption with a
method dubbed `agnostic stacking'. Using a forward-modelling framework we
combine this with direct detections in the literature to measure the overall
metal population. We apply this novel approach to the search for NeVIII
absorption in a set of 26 high-quality COS spectra. We probe to an
unprecedented low limit of log N$>$12.3 at 0.47$\leq z \leq$1.34 over a
pathlength $\Delta$z = 7.36. This method selects apparent absorption without
requiring knowledge of its source. Stacking this mixed population dilutes
doublet features in composite spectra in a deterministic manner, allowing us to
measure the proportion corresponding to NeVIII absorption. We stack potential
NeVIII absorption in two regimes: absorption too weak to be significant in
direct line studies (12.3 $<$ log N $<$ 13.7), and strong absorbers (log N $>$
13.7). We do not detect NeVIII absorption in either regime. Combining our
measurements with direct detections, we find that the NeVIII population is
reproduced with a power law column density distribution function with slope
$\beta = -1.86 \substack{+0.18 \\ -0.26}$ and normalisation log $f_{13.7} =
-13.99 \substack{+0.20 \\ -0.23}$, leading to an incidence rate of strong
NeVIII absorbers $dn/dz =1.38 \substack{+0.97 \\ -0.82}$. We infer a cosmic
mass density for NeVIII gas with 12.3 $<$ log N $<$ 15.0 of $\Omega _{NeVIII} =
2.2 \substack{+1.6 \\ _-1.2} \times 10^{-8}$, a value significantly lower that
than predicted by recent simulations. We translate this density into an
estimate of the baryon density $\Omega _{b} \approx 1.8 \times 10^{-3}$,
constituting 4\% of the total baryonic mass.
