Looking at that circuit, I'd guess the pot should be set so there is just under 0.6V on the base of the transistor when the conditions are static.
As the magnet swings over the coil a voltage should be induced which will increase the base voltage and trigger a pulse.
It's not a good circuit. I'd add a resistor in the base connection to the upper transistor, to start with.
I'd also try different orientations for the coil and magnet, it may be quite critical for the timing and polarity of the induced trigger and coil attraction or repulsion.
A very old pendulum device my brother once owned had a bar magnet attached to the centre of a long curved wire which formed the bottom of the pendulum - imagine a sixth of a circle outline with a curve and two radials made of wire, with the junction of the radials attached to the pendum swivel axle.
There was a tubular coil fixed to the frame, so the magnet was inside it at the centre position. The coil polarity was arranged to repel the magnet.
The "control" was just a thin springy wire from an insulated terminal on the frame and a metal blade or flag protruding from an attachment between the two radials.
There was a 1.5V D cell clipped in the base of the device. Each time the pendulum swung to the centre position the blade/flag touched the spring wire and stayed in contact with that for a very short distance, until it slipped past. That meant the coil always a pulse biassed to when the magnet was just past centre and the repulsion boosted the pendulum swing.
Edit - have a look at the circuits near the bottom of this page, they seem rather better than the one you found: