That’s that part I’m unclear on. Why stop modulating? It rather sounds like something foxhunters do in order to complicate the hunt by obscuring the location. Efficiency is nice but, to this beacon listener, distantly second to the objective of being heard.
In short, the periods of quiet amount to non-beaconing.
There’s no need to modulate the signal. The presence of the carrier is sufficient to demonstrate propagation. In fact, modulation complicates the purpose of a beacon signal.
A ‘dead’ carrier does not mean no signal. It just means no modulation.
Spectrum efficiency of an unmodulated continuous wave (CW) means the signal is stronger over a greater distance than a modulated carrier, and of consistent signal strength, making it a more effective form of transmission for a beacon. If you’re looking for a signal, its easier on an S meter to pin down the strength of a signal which is not being amplitude modulated.
As I said previously, an amplitude modulated carrier wastes 2/3 of its power on duplicating transmission of the other sideband and the carrier itself is superfluous in a modulated signal because it can be re-inserted in the receiver by the BFO.
A beacon signal is of best use as an unmodulated carrier, interrupted once per minute to send the callsign as identification. The grid square is usually sent after the callsign to make identification of the beacon location easier for the person looking for the beacon and divining the propagation conditions eg tropo or Es.
Clear now? 
73 de Brian VK2AAF
A signal I can’t hear is, from my station, indistinguishable from no signal. There are different ways of detecting signal and some need modulation. My own prior use of HF beacons needs something to listen for, audibly, as I roll past with the VFO and I won’t hear unmodulated carrier. But that’s ok, some stations will. In the end, it comes back to a bunch cool ham stuff I hope to be able to study in depth when I retire in 2097.
Thanks for your replies, I’m going to send you my call in a PM.
If your rig is in CW mode, the BFO is activated and you will hear a tone when you spin the dial past the beacon freq. If in AM, you will hear a quieting of background noise.