How can I light up 3 LEDs in sequence but only one at a time?
here is a mechanical way

just drag the lead across, contacting each LED in turn

not meant as an answer (it is the only way to include a schematic)







simulate this circuit &ndash; Schematic created using CircuitLab









simulate this circuit

A variation on the them. Use a ball-bearing running on two wire rails - one segmented with each LED connected to a segment - to switch the LEDs in sequence.