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Do you have a simple 12 V test light or a voltmeter with a reasonable knowledge of how to use it to check some voltages?
The 15 amp tail fuse which is located in the instrument panel on the left side of the dashboard control power to the taillight relay. When the taillights/headlight switch is turned on that 15 amp sends power to the taillight relay which turns on the illumination circuit and the running lights/taillights. Check this 15 fuse if you see if it's blown. when you turn the headlights on can you feel the taillight relay click on if the relays clicking on and you still do not have taillight it ispossible the relay could be bad. There's no way to know for certain without having some way to check for voltage is that specific point.
The next step is going to be checking for voltage to that fuse. If you do not have a voltmeter or simple 12 V test light there's no way I can give you a definitive answer. It's possible that the headlight switch is bad because that's what controls the circuit to ground for the relay. This is going to require at least a simple 12 V test light to check for voltage at the fuse and at the relay pins. Is that something you will be able to get from the local parts store?
If you look very closely at the 15 amp tail fuse there are two indentations on either side of the fuse make sure you have a good ground clamp I usually use a metal frame under the instrument panel or the door the door latch locks onto carefully probe these little indentations and touch little pieces of metal inside the fuse. Does that 15 amp fuse have 12 V to it
You asked me what was the next thing you needed to check that's what I just told you. I didn't expect you to give me an answer just yet you need to get a 12 V test light and check that and let me know the results.