Electromagnetic radiation from spark gap
Spark in a gap means that the current starts. There's often some light because the air in the gap is violently disturbed and the electrons in molecules get short term excitation. But the start of the current is the actual radiowave maker. The spectrum of the radiowave depends in a complex way on the waveform (=how fast the current starts) and the dimensions of the area where the current starts. That's because antenna theory shows the radiation intensity with a certain current strength and waveform depends on the dimensions of the area where the current occurs.
Unfortunately also the wires and the edges of the gap are a part of the system where the current suddenly starts. They can as well radiate. They also have capacitance and inductance which radically affect what's the actual waveform of the starting current. Early radio makers especially tried to initiate narrow band oscillations with sparks to get as sinusoidal radiation as possible. It helped to get design problems manageable.
People can present objections when I didn't mention voltage. It has as big role as current. In a gap generally the voltage collapses because the air becomes very conductive. But actually the interesting voltage is what's induced by the accelerating current. Static nor linearly growing current do not radiate.
Unfortunately there's no easy way to calculate the caused radiation, one must solve ultra complex space vector field differential equations. Antenna designers use either numerical methods or make approximations by dividing the current area to elementary dipoles. If you want to learn it prepare to study say one full days university level math to be able to understand it.
Your Oscilloscope image doesn't give any possibilities to even guess the generated radiation after assuming a certain gap because the interesting part - the rise of the current - is out of the resolution, it looks vertical. You have used far too slow equipment.
If your gap is the open end of a 2 parallel wire transmission line which is fed by a properly terminated voltage source you have a theoretical possibility to get radiation only from the gap with no resonances of the wires, but only in the usable frequency range of that transmission line. That radiation could be in theory be measured with a measurement antenna and spectrum analyzer.
Prepare to some real work because the receiver must be far away and its antenna must be small to prevent any phase difference problems due the distance differences between the parts of the gap and the parts of the receiving antenna. You must do a long integration to pull the noise levels down. You need non-echoing room.