When it worked, if it blinked with the turn signal or just glows with headlight makes a difference on where it grounds.
If side marker blinked as a turn signal, and glowed steady when headlights are on, both wires from the side marker are connected to the wires going to the front blinker/running light. That would mean the side marker bulb does not really have a separate ground, it just gets ground through the wiring that goes to the front bulb. So check the front blinker and running light are working correctly with headlights on and with headlights off, and check ground to that assembly. Replace bulbs in front blinker/running light if needed.
In the configuration where the side marker blinks as a turn signal, and glows steady when headlights are on, the polarity to the bulb reverses when headlights are on, so you should have special non-polarity-dependent LED bulbs to work. The plain 194 bulbs do not care about polarity, but many LED bulbs do care. Front LED bulbs could make the situation more complex regarding whether or not the side marker bulbs work, if you have a conventional 2-prong 194-type socket with reversing polarity for the side marker light.
If the side marker just glowed with headlights and was not part of blinker system, then track the ground wire from the side marker to find where it grounds and make sure there's a good connection. If you have to unwrap and re-wrap the wires that is OK and you can get that non-adhesive black vinyl tape in a new roll from Amazon and redo it. It takes patience but no special skill, except my skills at knotting the tape at the end of the run are not the best so I end up using a small zip tie.
