... I will need to buy a multimeter tomorrow ....
Pretty much any volt meter you can get will do for checking the voltage and connections on a car or MC, even the free ones they give away at Harbor Freight.
It does not have to be highly accurate. Even the ones they have at walmart for about $10 will tell you what you need to know.
Start by checking your battery, it should be close to 12V DC. When its freshly charged or the bike is running it will be around 12.5 to 12.8V. If you rev the engine up a bit it can jump over 13.5V, because the alternator is charging it.
You dont have to do all that looking for a problem with your running lights, just put the meter on the auto range DC V scale and see what it reads on the battery, of if it has manual ranges put it on the DCV 15 or 20V scale... whatever is the next scale higher than 12V.
If you have not used a meter before there are two things to be aware of:
OHMS. when you use it as an ohm meter to see if wires are connected, the circuit you are checking has to be off. For example if you want to check a bulb take it out of the socket and check the bulb separately. The ohm meter works by sending a small voltage thru the probes, if you have any power connected to the circuit the meter will wack out, or maybe be damaged.
AMPS. The amp meter function measures the current going thru the probes. When the probes are plugged into the amps jacks on the meter, the meter is a short circuit. If you put the meter on amps and then touch the probes to the battery, it will surge hundreds of amps thru the probes, and blow the fuse in the meter. If you want to measure how much current is going thru a circuit, like the headlight for example, you unhook one wire from the headlight, touch one probe to that wire and the other wire to the headlight terminal. Then the meter is in series, its completing the circuit that you just opened, and measures the current flowing thru the meter.
In general the way to find out why a light is not working: start at the battery, measure the 12V to show the meter is working, and you have a good ground, then work you way down the wiring towards the light that is out: battery terminal, fuse box, light switch, wire harness, fender connector, light socket.. and see where you lose the 12V.
If you have 12V at the light socket then the problem is the ground wire somewhere going back to the battery.