You will need two probes, or one plus a BNC cable or whatever.
Probe Ch1, serial pin to GND. Should be doing 0/5V or something like that, so 2V/div.
Check that it's reading the probe multiplier correctly, too, if applicable; the choice of 1x or 10x won't matter for this.
Ch2, RF input somehow. A 50dB coupler may be too quiet. How much does the radio key up when it's doing the test? Is that like some little pilot tone, or is it freaking full blast on a 100W transmitter? Mind that the inputs can't take more than maybe a watt, and that's probably pushing it. (my Tektronix actually has a thermistor to sense the temperature of the internal termination resistor, and disable it if it gets too hot... but I don't know if they bother with such features on a cheap scope like that.)
Trigger mode: single or normal; edge; source Ch1; whichever +/- slope you need (you'll know better, having wired the contact closure); threshold/level halfway between voltage/logic levels.
Horizontal: probably 2ms/div is a good starting point. Repeat the test a few times until you see what you're looking for.
Display mode / acquisition: peak detect mode. Not High Res, or bandwidth limiting, or smoothing, or averaging, or any of that. (BW settings are often under the vertical/channel menus too.)
Also, obviously, your scope needs to be able to resolve the frequency you're running at. So, a 100MHz scope will see shortwave signals just fine, and probably won't be remarkably useful troubleshooting VHF radios (you don't have enough bandwidth to resolve harmonic distortion, if present) but will still detect it, and anything UHF+ will just buzz right on past without a clue. (For those cases -- you can use an RF detector probe, in which case your Ch2 will see a DC offset when RF is present, so Peak Detect mode won't matter.)
Tim