Here is a simple DIY LED continuity tester circuit which can be built in few minutes using only two components a 390 Ohms resistor and LED. This continuity test circuit can be used for testing components, wires, connection, PCB tracks etc. Use two test probes with the circuit to test.
When you connect the two probes with any item under test then the current will circulate around that item and light up the LED. Use 9V battery with the circuit.