Individual optical emitters coupled via coherent interactions are attractive qubits for quantum communications applications. Here, we present the first study of single pairs of interacting rare earth ions and determine the interactions between ions in the pair with high resolution. We identify two examples of Er3+ pair sites in Er implanted Si and characterise the interactions using optical Zeeman spectroscopy. We identify one pair as two Er3+ ions in sites of at least C-2 symmetry coupled via a large, 200 GHz, Ising-like spin interaction in both optical ground and excited states. The high measurement resolution allows non-Ising contributions to the interaction of <1% to be observed, attributed to site distortion. By bringing two optical transitions into resonance with a magnetic field, we observe a 0.8 GHz optical interaction of unusual magnetic-dipole/electric-dipole character with strong polarization selection rules. We discuss the use of this type of strongly coupled, field-tunable rare earth pair system for quantum processing.