To be most effective, where should a low-pass filter be connected in an HF station without an external power amplifier?

A low-pass filter is designed to let low frequencies (like your HF operating frequency) pass through while blocking higher frequencies (like harmonics that cause interference). To prevent these unwanted harmonic signals from radiating out through the connecting cables or other equipment, the filter must be placed right at the source of the high-power RF signal. In a station without an external amplifier, the transceiver itself is the final source of the amplified RF signal. Connecting the filter as close as possible to the transceiver output ensures that any harmonics generated by the radio are stopped immediately before they can travel down the feedline to the antenna tuner, SWR meter, or antenna. Placing it further down the line, such as near the antenna tuner or switch, allows the intermediate coaxial cables to act as radiating antennas for the harmonics, which defeats the entire purpose of the filter.