Most HF DF equipment can be used on SSB, at least in manual mode.
You can'd DF the station when the operator isn't talking, of course,
because there isn't any power output (unless the signal is strong enough
that you can hear the suppressed carrier or some background noise.)
But that doesn't mean you can't still take a bearing.
I got started in DF many years ago hunting SSB on 75m with a loop.
You kept turning the loop back and forth to hear the null while the
operator was talking and waited during pauses. Now I use a hand-held
DF receiver on keyed CW and the situation is similar: I can only take
a bearing when the transmitter is on, but with mental averaging I can
find that point fairly easily. It does, however, require a slower sweep
than can be used on a continuous carrier.
(Or a faster sweep if that means I can cover the whole range of interest
in the time of one DAH on CW. Most of the time I know the rough
direction and am simply refining the bearing.)
Note that all of this is done by watching the S meter or (preferably)
listening to signal strength by ear, so I'm using my built-in signal
processor rather than an external electronic one. Though with an ADF
system it should rotate while the operator is talking and stop during
pauses (depending on the time constants) and it may still be able to
give a good bearing if you are willing to wait a bit.
If you want a more elaborate system, the Watson-Watt method will give
an instantaneous readout, even on a varying signal. In theory it requires
two receivers (and a third for sense) that are exactly matched in phase
and amplitude response. Modern implementations use a single receiver
and modulate the antenna inputs so the resulting signals can be sorted
out later. The readout is a line on an oscilloscope face that is calibrated
in degrees around the perimeter. I wonder if that is the type you were
using when you talked about watching the CRT?
Systems that switch between two antennas will have problems unless
the switching speed is very high. Methods that compare the phase
between two antennas in real-time should still work on an SSB signal,
though the time constants may require adjustment. Rotating a simple
loop for a null is probably hard to automate, since it is difficult for the
hardware to tell the difference between a null and a pause in speech
(unless there is a reference non-directional antenna as well) but can
work just fine using the processor between your ears.