The hydrocarbon wells include a radioactive tracer system, a production conduit, a lift gas supply conduit, a lift gas supply system configured to provide a lift gas stream to the lift gas supply conduit, and one or more gas lift valves each being configured to selectively permit lift gas to enter the production conduit and mix with reservoir liquid therein to generate a produced fluid stream. The radioactive tracer system is configured to inject a radioactive tracer into the lift gas stream and to detect the radioactive tracer within the produced fluid stream. The methods include injecting the radioactive tracer into the lift gas stream, flowing the radioactive tracer through an open gas lift valve into the production conduit, mixing the radioactive tracer with the reservoir liquid to generate a tracer-marked liquid band within the produced fluid stream, and detecting radiation from the tracer-marked liquid band.