Microburst - let me give this a try. I am not familiar with what you to refer to as the "so called second mode". I googled it, but did not get much. Is that another name for the "short period".
The basic longitudinal dynamics of a rigid body airplane are customarily presented as having four states: U (speed), Alpha (angle-of-attack), q (pitch rate), and theta (pitch angle). These four states give rise to two modes: phugoid and short period. Phugoid can be thought of as a constant energy mode where speed and altitude are trading back and forth (tranfer between kinetic and potential energy). Phugoid frequency is usually quite slow with a period of 30 seconds to two minutes. Short period can be though of as a constant speed mode with a much higher frequency with a period of a couple of seconds.
When the elevator is deflected it excites both the short period and the phugoid modes. The short period is much faster so it dominates the initial response. The airplane pitches until the restorative pitching moment generated by a change in angle of attack balances the pitching moment from the elevator (assuming stability). This results in the relationship between stick force and normal load factor as the angle of attack change gives rise to lift change. As you state, this initial response takes only a couple of seconds and hopefully the short period mode has sufficient damping to settle out to a steady load factor quickly.
Now as time goes on the phugoid comes into play due to the load factor change causing a flight path change and thus a speed change (assuming constant thrust). The phugoid is driven by the pitching moment associated with a change in speed. Note that the phugoid mode for a large transport airplane is usually quite lightly damped. Because it is so slow, however, the pilot is able to add damping without much trouble.
Short period stability is closely related to Cm-alpha (pitching moment due to angle of attack). With the airplane CG well forward, Cm-alpha is large and it will take lots of elevator (i.e., stick force) to hold a target load factor. As CG moves aft, Cm-alpha is reduced and stick force per g goes down. Go far enough and you get neutral stability where a steady pull-up load factor can be achieved with the stick back at zero. Go even farther and you have a whale of a ride on your hands as the short period is unstable. Every little disturbance will push that airplane away from pitch trim and corrective action will be required to bring it back! How would you find only needing a small pull to start the nose up and then having to push to keep load factor for increasing to the point where you either stall or break the wing?!
With C* augmentation the phugoid mode is eliminated by the control system that controls to a target pitch rate / normal load factor maneuver. To get C*U, speed feedback is added to create what is essentially an augmentation phugoid. The period of that augmentation phugoid is determined by how much gain is placed on the speed feedback path. The higher the gain, the shorter the period of the phugoid mode.
Sorry to ramble on, but I enjoy discussions that bring it back to the physics. If you really want to make it interesting start taking the flexible modes of the airplane structure into account!