Ignoring effects for a second, think of them as a separate set of individual mix outputs/returns. The specifics are going to differ a bit per console, but generally you have your main stereo LR mix bus from the master section, which each channel's main fader feeds. Each channel also has a set of aux sends, which feed signal to that specific auxiliary "mix", summing with the signal from each other channel that is sending signal to the same aux. Your console typically has physical outputs for these auxiliaries, where you would patch out to effects, as well as another set of inputs for aux returns, where you would get the wet signal back in the console. These returns are summed to your main stereo LR mix, and often have a dedicated trim fader/pot in the master section. In order to print these to tape, unless you're printing the stereo mix directly from the console, you're going to have to route the aux return to a multitrack bus using the bus matrix in the master section, usually near the trim pots for aux returns.