Despite the well-known limitations of linear stability theory in describing nonlinear and turbulent flows, it has been found to accurately capture the transitions between certain nonlinear flow behavior. Specifically, the transition in heat flux scaling in rotating convective flows can be well predicted by applying a linear stability analysis to simple profiles of a convective boundary layer. This fact motivates the present study of the linear mechanisms involved in the stability properties of simple convective setups subject to rotation. We look at an idealized two-layer setup and gradually add complexity by including rotation, a bounded domain, and viscosity. The two-layer setup has the advantage of allowing for the use of wave interaction theory, traditionally applied to understand stratified and homogeneous shear flow instabilities, in order to quantify the various physical mechanisms leading to the growth of convective instabilities. We quantitatively show that the physical mechanisms involved in the stabilization of convection by rotation take two different forms acting within the stratified interfacial region, and in the homogeneous mixed layers. The latter of these we associate with the tendency of a rotating flow to develop Taylor columns (TCs). This TC mechanism can lead to both a stabilization or destabilization of the instability and varies depending on the parameters of the problem. A simple criterion is found for classifying the influence of these physical mechanisms.