All you need is a lightbulb a piece of wire with crocodile clip long enough reach battery earth and test area and a nice pointy screw, nail or wire to make a quick diy test light which super handy for power side testing .
first thing do is quick test for power at the LH 15amp fuse that feeds to the column light switch (although this obviously should be fine as it feed main beam also and that works but good be 120% sure power is being fed from fusebox)
2nd thing do is quick test of power at dip power wire to back of headlight (they normally play up right near the plug if wiring) and give that wire a bit of visual check and wiggle test.
3rd thing test is the column switch * and this is what I expect it likely be if headlight and car wiring not been butchered by previous owners *
LH one tends always be column switch issue (burnt switch contacts) if plug wiring at headlamp in good order and high beam works .
Don't rely too much on continuity testing switch power side circuits, while continuity is super useful it quicker diagnose stuff like yours on power side with a test light first as super fast and cheap plus a circuit best tested under load as it can show continuity yet not handle required current .