How to trigger a "Relay Module With OPTO Isolation Support High or Low Level Trigger" with a momentary switch
I think you're overcomplicating things with the pre-fab, does-all relay module.  That module is probably this:







simulate this circuit &ndash; Schematic created using CircuitLab

And to answer your original question, the part you're missing is R1 to bias it towards whichever DC rail you connect it to.  I've drawn it as a pull-up because of tradition, in which case the controlling switch would go between IN and DC-.

But all you really need is this:







simulate this circuit

If the controlling switch S1 controls to the negative side instead, that works too; the order doesn't matter as long as you know it and design accordingly.

The relay itself provides the isolation, but I'm not convinced that you actually need it:


If the controlled switch and the controlling switch both switch to ground (see the note on my first schematic) and they both have the same ground, then you only need one wire in theory, straight across.  The return current would flow through the common ground, which would technically cause a slight error in the ground voltage, which is what causes ground loop noise...but only if that current has audible frequencies in it.  This is DC, which you can't hear and the equipment should reject anyway.  Maybe it clicks when you press and/or release it, but that would be all.
If the controlling switch is already isolated, then you don't even have that problem.  Just run two wires straight across and be done.




About the diode, D1, in both schematics: The circuits may work without it...for a while.  But because you can't stop the current instantly through the relay coil, being an inductive device by necessity, it will generate whatever voltage it needs to keep that current flowing until the energy dies away.  D1 provides a path to do that without requiring crazy high voltages (hundreds, maybe thousands of volts, briefly) that may eventually destroy a switch (and certainly a transistor, Q1), which the relay will happily do if that's what it takes to keep the current flowing.  Any old diode will do, provided that its maximum reverse voltage is more than the relay's operating voltage.