Many membrane-bound T cell receptors have long, unstructured cytoplasmic tails that contain tyrosine sites. These sites can serve as regulators of receptor activation when phosphorylated or dephosphorylated, while also serving as docking sites for cytosolic enzymes. Interactions between receptors then involve the in-membrane diffusion of the receptor proteins, and reactions between proteins tethered to the receptors' tails (and hence diffusing within the three-dimensional cytosolic space near the membrane). We develop a particle-based stochastic reaction-diffusion model based on the Convergent Reaction-Diffusion Master Equation to study the combined diffusion of individual receptors within the cell membrane, and chemical reactions between proteins bound to receptor tails. The model suggests a switch-like behavior in the dependence of the fraction of activated receptors on both receptor diffusivity, and on the molecular reach at which two receptor tails can interact. A simplified, analytically solvable model is developed to approximate the more complicated multi-particle system, and used to illustrate how the switch-like behavior arises.