I get the light house analogy, and how the VOR essentially works, although I'm wondering what actually causes this phase shift? As it hits magnetic north the variable and reference signal are in phase, as it continues it begins to go out of phase. What's causing it to go out of phase? Is it using constant frequency modulation, where both are being constantly modulated, and at a certain point they both hit the same frequency for a second?
The modulation of the variable (position) signal is actually the amplitude of this signal at the receiver. The amplitude varies because the position signal, a constant power carrier with no modulation, is sent by a directional antenna rotating at 1,800 RPM (30 Hz).
The antenna system is usually composed of 5 vertical elements, 4 at the corner of a square, and the last in the middle, but not at the exact center, so that the radiation pattern is not omnidirectional. The signal is maximum when the antenna faces the direction of the receiver. The radiation pattern is a cardioid:
A second signal, the reference, is sent by the center antenna, equally in all directions. It carries a 30 Hz signal (on a 9,960 Hz FM sub-carrier) which starts at 0 when the rotating antenna faces North. This reference modulation then varies according a sine function at 30 Hz.
All 5 radiators are located under a vertical radome which looks like a TACAN, for the reason the VOR is derived from the TACAN (more about what's inside the radome in this answer).
Thales conventional VOR 431, source
The 8 small antennas are not part of the VOR, they are for monitoring its integrity
The receiver sees two modulations: The FM modulation of the reference and the pseudo-AM modulation of the position signal created by the rotation of the VOR antennas. If the receiver is North of the VOR, it sees the two modulations in phase, and a difference appears for all other receiver azimuths.
To link with your lighthouse analogy, imagine there are two lights:
- A white reference light which blinks shortly every second
- A green rotating signal which is facing North when the white light blinks, and turns 360° between two white flashes.
We just need to measure the lag of the green light relative to the white light to know our relative bearing from the station.
If the lights intensity increases and decreases smoothly instead of just appearing briefly, we obtain the modulations used in a VOR. The time for a rotation is actually 1/30ths.
Modern VOR are Doppler VOR. There is no difference for the receiver. The position signal is not produced by a rotating antenna, but by a circular array of fixed antennas.
Thales Doppler VOR 432, source
In the D-VOR each antenna radiates a signal which is a bit different in phase, according to the position signal.
The sum of all signals produces a rotating radiation pattern (a "limaçon", French word for conch) similar in amplitude to the C-VOR position carrier.
This is done in a way that, when related to the diameter of the antenna array, a Doppler (frequency) shift appears. This shift is equivalent to the 30 Hz FM modulation of the reference signal of a C-VOR.
The receiver can't tell the difference. However the fact that FM is used in place of AM for the position signal increases the angular precision.