We compare mass-selected close pairs at z > 1 with the intrinsic galaxy merger rate in the Illustris Simulations. To do so, we construct three 140 arcmin^2 lightcone catalogs and measure pair fractions, finding that they change little or decrease with increasing redshift at z > 1. Consistent with current surveys, this trend requires a decrease in the merger-pair observability time, roughly as (1 + z)^-2, in order to measure the merger rates of the same galaxies. This implies that major mergers are more common at high redshift than implied by the simplest arguments assuming a constant observability time. Several effects contribute to this trend: (1) The fraction of massive, major (4:1) pairs which merge by today increases weakly from ~0.5 at z=1 to ~0.8 at z=3. (2) The median time elapsed between an observed pair and final remnant decreases by a factor of two from z~1 to z~3. (3) An increasing specific star formation rate (sSFR) decreases the time during which common stellar-mass based pair selection criteria could identify the mergers. The average orbit of the pairs at observation time varies only weakly, suggesting that the dynamical time is not varying enough to account by itself for the pair fraction trends. Merging pairs reside in dense regions, having overdensity ~10 to ~100 times greater than the average massive galaxy. We forward model the pairs to reconstruct the merger remnant production rate, showing that it is consistent with a rapid increase in galaxy merger rates at z > 1. ; Comment: submitted to MNRAS, 9 pages, 9 figures